What Makes a System Complex? - An Approach to Self Organization and Emergence

  • Michel Cotsaftis
Part of the Understanding Complex Systems book series (UCS)


The fast changing reality in technical and natural domains perceived by always more accurate observations has drawn the attention on a new and very broad class of systems mainly characterized by specific behavior which has been entered under the common wording ”complexity”. Based on elementary system graph representation with components as nodes and interactions as vertices, it is shown that systems belong to only three states : simple, complicated, and complex, the main properties of which are discussed. The first two states have been studied at length over past centuries, and the last one finds its origin in the elementary fact that when system performance is pushed up, there exists a threshold above which interaction between components overtake outside interaction. At the same time, system self-organizes and filters corresponding outer action, making it more robust to outer effect, with emergence of a new behavior which was not predictable from only components study. Examples in Physics and Biology are given, and three main classes of ”complexity” behavior are distinguished corresponding to different levels of difficulty to handle the problem of their dynamics. The great interest of using complex state properties in man-made systems is stressed and important issues are discussed. They mainly concentrate on the difficult balance to be established between the relative system isolation when becoming complex and the delegation of corresponding new capability from (outside) operator. This implies giving the system some ”intelligence” in an adequate frame between the new augmented system state and supervising operator, with consequences on the canonical system triplet effector-sensorcontroller which has to be reorganized in this new setting. Moreover, it is observed that entering complexity state opens the possibility for the function to feedback onto the structure, ie to mimic at technical level the invention of Nature over Her very long history.


Complicated Systems Complex Systems Self-Organization Emergence Invariance Nonlinear Control of Natural and Man-made Systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Descartes, R.: Le Discours de la Méthode. Œuvres, V. Cousin, (ed.), Paris (1824)Google Scholar
  2. 2.
    Pattee, H.H.: Hierarchy Theory, the Challenge of Complex Systems. Braziller, New York (1973) Galbraith, J.: Designing Complex Organizations. Addison Wesley, Reading (1973) Cottrell, A.: Emergent Properties of Complex Systems. In: Duncan, R., Weston Smith, M. (eds.) Encyclopedia of Ignorance, pp. 129–135. Pergamon Press, Oxford (1977) Simon, H.A.: How Complex are Complex Systems? Philosophy of Science Assoc. 2, 507–522(1976) Hayek, F.A.: The Theory of Complex Phenomena. In: Bunge, M. (ed.) The Critical Approach to Science and Philosophy. Collier McMillan, London, pp. 332–349 (1964) Walker, C.C.: Behavior of a Class of Complex Systems: the Effect of Systems Size on Properties of Terminal Cycles. J. of Cybernetics 1, 55–67 (1971) Ferdinand, A.E.: Complex Systems are Those that Work Even with Maximum Entropy. Intern. J. of General Systems 1, 19–33 (1974) Nelson, R.J.: Structure of Complex Systems. Philosophy of Science Association 2, 523–542 (1976) Casti, J.L.: Complexity, Connectivity and Resilience in Complex Ecosystems. In: IFAC Symp. on Bio and Ecosystems, Liepzig, Germany (1977) Trappler (ed.): Power, Autonomy, Utopia: New Approaches towards Complex Systems. Plenum Press, New York (1986) Johnson, J.: A Theory of Stars in Complex Systems. In: Casti, J.L., Karlquist, A. (eds.) Complexity, Language and Life: Mathematical Approaches, pp. 21–61. Springer, Berlin (1986) Haken, H.: Information and Self Organization: a Macroscopic Approach to Complex Systems. Springer, Berlin (1988) Soodak, H., Iberall, A.S.: Thermodynamics and Complex Systems. In: Yates, F.E.(ed.) Self-Organizing Systems: the Emergence of Order, pp. 459–469. Plenum Press, New-York (1987) Dyke, C.: The Evolutionary Dynamics of Complex Systems. OUP, New York (1988) Funtowicz, S. Ravetz, J.: Emergent Complex Systems. Futures 26, 568–582 (1994) Wolfram, S.: Complex Systems Theory. In: Pines, D. (ed.)Emerging Syntheses in Science, pp. 183–190. Addison Wesley, Redwood City (1987) Haken, H.: Synergetics: An Introduction, 2nd edn. Springer Series in Synergetics, vol. 1. Springer, Heidelberg (1983) Haken, H.: Information and Self-Organization: A Macroscopic Approach to Complex Systems. Springer Series in Synergetics, vol. 40. Springer, Heidelberg(1988) Google Scholar
  3. 3.
    Weinberg, S.: Dreams of a Final Theory. Pantheon Books, New-York (1993)Google Scholar
  4. 4.
    Laughlin, R.: A different Universe: Reinventing Physics from the Bottom Down. Basic Books, New-York (2005)Google Scholar
  5. 5.
    Laplace, P.S.: OEuvres Complètes. Part 6. Gauthiers Villard, Paris (1878-1912) Lagrange, J.L.: Mécanique Analytique, vol. I-II. Ed. Albert Blanchard, Paris (1788)Google Scholar
  6. 6.
    Aritotle (circa 340 BC) ”Physics”, Part I, ch. 9 Anderson, P.W.: More is Different. Science 177, 393–396 (1972)Google Scholar
  7. 7.
    Gell-Mann, M.: What is Complexity? Complexity 1, 16–19 (1995) Nicolis, G., Nicolis, C.: Foundations of Complex Systems. World Scientific Pub., Singapore (2007) Weaver,W.: Science and Complexity. American Scientist 36, 536–544 (1948) Nicolis, G., Prigogine, I.: Exploring Complexity : an Introduction. W.H. Freeman and Co, New-York (1989) Bunge, M.: The Myth of Simplicity. Prentice Hall, Englewood Cliffs (1963) Ashby, W.R.: Introduction to Cybernetics. Methuen, New-York (1964) Baldwin, M.: Portraits of Complexity. Battelle Memorial Institute, Ohio (1975) Traub, J.F., Wasilkowski, G.W., Wozniakowski, H.: Information, Uncertainty, Complexity. Addison Wesley, Reading (1983) Casti, J.L.: Connectivity, Complexity and Catastrophe. J. Wiley and Sons, New-York (1979) Cornacchio, J.V.: System Complexity - A Bibliography. Intern. J. of General Systems 3, 267–271(1977) Warfield, J.N.: Planning, Policy, and Complexity. J. Wiley and Sons, New-York (1976) Prigogine, I., Stengers, I.: Order Out of Chaos - Man’s New Dialogue with Nature. Bantam Books, Toronto (1984) Grunberg, E.: “Complexity” and “Open Systems” in Economic Discourse. J. of Economic Issues 12, 541–560(1978) Brewer, G.D.: Analysis of Complex Systems: An Experiment and its Implications for Policy Making. Rand Corp. Report, P-4951, Santa Monica, CA (1973) Van Emden, M.H.: An Analysis of Complexity. Mathematical Centre Tracts. Mathematische Centrum Amsterdam, Amsterdam (1971) Ashby, W.R.: Some Peculiarities of Complex Systems. Cybernetic Medicine 9, 1–7 (1973) Kemeny, J.G.: Two Measures of Complexity. The Journal of Philosophy 52, 722–733 (1955) Winograd, S.: Redundancy and Complexity of Logical Elements. Information and Control 5, 177–194 (1963) Hillel, B. Kasher, Y. Shamir, E.: Measures of Syntactic Complexity. In: Booth, A.D. (ed.) Machine Translation, pp. 30–50. North Holland, Amsterdam (1967) Moshowitz, A.: Entropy and the Complexity of Graphs. Bull. Mathematical Biophysics 30, 175–204, 225–408 (1968) Rock, R.A.: Integrative Complexity and Non-Specific Set as Determinants of Performance in a Complex Solving Task. J. Behavioral Science 1, pp. 17–25 (1969) Zvonkin, A.K., Levin, L.A.: The Complexity of Finite Objects and the Development of the Concepts of Information and Randomness by Means of the Theory of Algorithms. Russian Math. Surveys 256, 83-124 (1970) Beer, S.: Managing Modern Complexity. Futures 2, 245–257 (1970) Ausiello, G.: Abstract Computational Complexity and Cycling Computations. J. Computer and System Sciences 5, 118–128 (1971) Sober, E.: Simplicity. Clarendon Press, Oxford (1975) Wimsatt, W.: Complexity and Organization. In: Schaffner, K., Cohen, R.(eds.) Studies in the Philosophy of Sciences, pp. 67–86. Reidel, Dordretch (1972) Cilliers, P.: Complexity and Post-modernism. Routledge, London (1998) Feldman, J.A.: Some Decidability Results on Grammatical Inference and Complexity. Information and Control 20, 244–262 (1972) Seaman, J.M., Koenig, F.: A Comparison Measures of Cognitive Complexity. Sociometry 37, 375–390 (1974) Rosen, B.K.: Syntactic Complexity. Information and Control 24, 305–335 (1974) Morin, E.: Complexity. Intern. J. of Social Science 26, 583–597 (1974) Lofgren, L.: Complexity of Descriptions of Systems: A foundational Study. Intern. J. of General Systems 3, 197–214 (1974) Arbib, M.A., Manes, E.G.: Foundations of System Theory: Decomposable Systems. Automatica 10, 285–302 (1974) Bremermann, H.: Complexity of Automata, Brains and Behavior. Lecture Notes in Bio Mathematics 4, 304–331 (1974) Gottinger, H.W.: Complexity and Information Technology in Dynamic Systems. Kybernetics 4, 129–141 (1975) Pippenger, N.: Complexity Theory. Scientific American 239, 90–100 (1978) Futia, C.: The Complexity of Economic Decision Rules. J. Mathematical Economics 4, 289–299 (1975) De Luca, A.: Complexity and Information Theory. In: Longo, G. (ed.) Coding and Complexity, pp. 207–270. Springer, Berlin (1975) Yokoyama, T.: Complexity and Hierarchy Theory. Osaka Economic Papers 26, 26–34 (1976) Simon, H.A.: The Architecture of Complexity. In: The Sciences of the Artificial, pp. 192–229. MIT Press, Cambridge (1981) Sahal, D.: Elements of an Emerging Theory of Complexity Per Se. Cybernetica 19, 5–38 (1976); System Complexity: Its Conceptions and Measurement in the Design of Engineering Systems. IEEE Trans. on Systems, Man and Cybernetics 6, 440–445 (1976) Auyang, S.Y.: Foundations of Complex-System Theories. Cambridge University Press, Cambridge (1998) Holland, J.: Hidden Order: How Adaptation Builds Complexity. Helix Books/Addison Wesley, New-York (1995) Waldrop, M.: Complexity: the Emerging Science at the Edge of Order and Chaos. Touchstone, New-York (1993) McCabe, J.: A Complexity Measure. IEEE Trans. on Software Engineering 2, 308–320 (1976) Gottinger, H.W.: Complexity and Dynamics: Applications of Dynamic Systems Theory. IEEE Trans. on Systems, Man and Cybernetics 6, 867–873 (1976) Gaines, B.R.: System Identification, Approximation and Complexity. Intern. J. of General Systems 3, 145–174 (1977) Rosen, R.: Complexity and System Descriptions. In: Harnett, W.E. (ed.) Systems: Approaches, Theories, Applications, pp. 169–175. Reidel, Dordrecht (1977) Marcus, M.J.: The Theory of Connecting Networks and their Complexity: A Review. Proc. IEEE 65, 1263–1271 (1977) Goguen, J.A.: Complexity of Hierarchically Organized Systems. Intern. J. of General Systems 3(4), 233–251 (1977) George, B.: Tests for System Complexity. Intern. J. of General Systems 3, 253–257 (1977) Yates, F.E.: Complexity and the Limits to Knowledge. Amer. J. of Physiology 235, R201–R204 (1978) Solomonoff, R.J.: Complexity-Based Induction Systems: Comparisons and Convergence Theorems. IEEE Trans. on Information Theory 24, 422–432 (1978) Klir, G.J.: Complexity: Some General Observations. Systems Research 2, 131–140 (1985) Pearl, J.: On the Connection Between the Complexity and Credibility of Inferred Models. Intern. J. of General Systems 4, 255–264 (1978) Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison Wesley, Reading (1979) Levine, R.D., Tribus, M. (eds.): The Maximum Entropy Principle. MIT Press, Cambridge (1979) Rouse, W.B., Rouse, S.H.: Measures of Complexity of Fault Diagnosis Tasks. IEEE Trans. on Systems, Man and Cybernetics 9, 720–727 (1979) Gershenson, C., Heylighen, F.: How Can we Think the Complex? In: Richardson, Kurt (eds.) Managing the Complex: Philosophy, Theory and Application, vol. 1. Institute for the Study of Coherence and Emergence/Information Age Publishing (1987) Papentin, F.: On Order and Complexity. J. Theoretical Biology 87, 1–456 (1980) Albin, P.S.: The Complexity of Social Groups and Social Systems by Graph Structures. Mathematical Social Sciences 1, 101–129 (1980) Dussauchoy, R.L.: Generalized Information Theory and the Decomposability of Systems. Intern. J. of General Systems 9, 13–36 (1982) Albin, P.S., Gottinger, H.W.: Structure and Complexity in Economic and Social Systems. Math. Social Sciences 5, 253–268 (1983) Hinegardner, R., Engelberg, J.: Biological Complexity. J. Theoretical Biology 104, 7–20 (1983) Ziv, J.: Complexity and Coherence of Sequences. In: Durand, H., di Lullo, M., Sinclair, C. (eds.) The Impact of Data Processing Techniques on Communications, Nijhoff, Dordrecht, pp. 23–33 (1983) Wolfram, S.: Universality and Complexity in Cellular Automata. Physica D 10, 1 (1984); Computational Theory of Cellular Automata, Comm. Mathematical Physics 96, 15–57 (1984); Cellular Automaton as Models of Complexity. Nature 311, 419–424 (1984) Aida, et al. (eds.): The Science and Praxis of Complexity. United Nations University, Tokyo (1984) Prather, R.E.: An Axiomatic Theory of Software Complexity Research. The Computer J. 27, 340–346 (1984) Nerisian, A.: On a Definition of the Description Complexity of Finite Systems. Intern. Inst. for Applied Systems Analysis, Rept. WP-84-004 (1984) Rosen, R.: Anticipatory Systems. Pergamon Press, New-York (1985) Lovsz, L.: The Mathematical Notion of Complexity, Inst. fur Okonometrie und Operations Research Report, University of Bonn, Germany (1985) Ho, J.K.K., Sculli, D.: System Complexity and the Design of Decision Support Systems. Systems Practice 8, 505–516 (1995) Rosen, R.: Organisms as Causal Systems which are not Mechanisms: An Essay into the Nature of Complexity. In: Rosen, R. (ed.) Theoretical Biology and Complexity: Three Essays on the Natural Philosophy of Complex Systems, pp. 165–203. Acad. Press, London (1985) Casti, J.L., Karquist, A. (eds.): Complexity, Language and Life: Mathematical Models. Springer, Berlin (1985) Celluci, C.: Proof Theory and Complexity. Synthese 62, 173–189 (1985) Bonner, J.T.: The Evolution of Complexity. Princeton Univ. Press, Princeton (1988) Bennett, C.H.: Dissipation, Information, Computational Complexity and the Definition of Organization. In: Pines, D. (ed.) Emerging Syntheses in Science, pp. 215–233. Addison-Wesley, Redwood City (1985) Wood, R.E.: Task Complexity: Definition of the Construct. Organizational Behavior and Human Decision Processes 36, 60–82 (1986) Huberman, B.A., Hogg, T.: Complexity and Adaptation. Physica D 22, 376–384 (1986) Grassberger, P.: Towards a Quantitative Theory of Self-Generated Complexity. Intern. J. of Theoretical Physics 25(9), 907–938 (1986) Bennett, C.H.: On the Nature and Origin of Complexity in Discrete, Homogenous, Locally-Interacting Systems. Foundations of Physics 16, 585–592 (1986) Kampis, G., Csanyi, V.: Notes on Order and Complexity. J. of Theoretical Biology 124, 111–121 (1987) Koppel, M.: Complexity, Depth and Sophistication. Complex Systems 1, 1087–1091 (1987) Gottinger, H.W.: Choice and Complexity. Mathematical Social Sciences 14, 1–17 (1987) Flood, R.L., Carson, E.R.: Dealing with Complexity. Plenum Press, New-York (1988) Mainzer, K.: Complex Systems in Nature and Society. Physik in Unserer Zeit 28, 74–81 (1997); Thinking in Complexity: The Complex Dynamics of Matter, Mind, and Mankind, 3rd edn. Springer, Heidelberg (1997) Levesque, H.J.: Logic and the Complexity of Reasoning. J. of Philosophical Logic 17, 355–389 (1988) Campbell, D.J.: Task Complexity: A Review and Analysis. Academy of Management Review 13, 40–52 (1988) Turney, P.: The Architecture of Complexity: A New Blueprint. Synthesis 79, 515–542 (1989) Stein, D.: Lectures in the Sciences of Complexity. Addison Wesley, Redwood City (1989) Berger, E.: Computability, Complexity, Logic. North Holland, Amsterdam (1989) Badii, R.: Unfolding Complexity in Nonlinear Dynamical Systems. In: Abraham, N.B. (ed.) Measures of Complexity and Chaos, pp. 313–325. Plenum Press, New-York (1989) Turney, P.: Problems with Complexity in Gold’s Paradigm of Induction– Part I: Dynamic Complexity. Intern. J. of General Systems 17, 329–342 (1990); Part II: Static Complexity. IBID, 343–358 (1990) Rustem, B., Velupillai, K.: Rationality, Computability and Complexity. J. of Economic Dynamics and Control 14, 419–432 (1990) Kindlmann, P.: Stability vs. Complexity in Model Computational Communities. Lecture Notes in Bio-Mathematics 54, 191–207 (1984) d’Alessandro, G., Politi, A.: Hierarchical Approach to Complexity with Applications to Dynamic Systems. Phys. Rev. Letters 64, 1609–1612 (1990) Banks, J.F., Sundaram, R.K.: Repeated Games, Finite Automata and Complexity. Games and Economic Behavior 2, 97–117 (1990) Machlin, R.: The Complex Behavior of Simple Machines. Physica D 42, 85–98 (1990) Gorodkin, J., Sorensen, A., Winther, O.: Neural Networks and Cellular Automata Complexity. Complex Systems 7, 1–23 (1993) Lloyd, S.: Physical Measures of Complexity. In: Jen, E. (ed.) Lectures in Complex Systems, pp. 67–73. Addison Wesley, Reading (1990) George, D.A.R.: Chaos and Complexity in Economics: Review Article. J. of Economic Surveys 4, 397–404 (1990) Bennett, C.H.: How to Define Complexity in Physics, and Why. In: Zurek, W.H. (ed.) Complexity, Entropy and the Physics of Information, pp. 137–148. Addison Wesley, Redwood City (1990) Balcazar, J.L.: Structural Complexity. Springer, Berlin (1990) Baker, G.L.: Chaotic Dynamics. Cambridge Univ. Press, Cambridge (1990) Traub, J.F., Wozniakowski, H.: Information-Based Complexity: New Questions for Mathematicians. Mathematical Intelligencer 13, 34–43 (1991) Zuse, H.: Software Complexity. Walter de Gruyter, Berlin (1991) Lakshmanan, K.B., Jayaprakash, S., Sinha, P.K.: Properties of Control-Flow Complexity Measures. IEEE Trans. on Software Engineering 17, 1289–1295 (1991) McShea, D.: Complexity and Evolution: What Everybody Knows. Biology and Philosophy 6(3), 3003–3024 (1991) Kampis, G.: Self-Modifying Systems in Biology and Cognitive Science: A New Framework for Dynamics. Information and Complexity. Pergamon Press, Oxford (1991) Grassberger, P.: Information and Complexity Measures in Dynamical Systems. In: Atmanspacher, H., Scheingraber, H. (eds.) Information Dynamics, pp. 15–33. Plenum Press, New-York (1991) Woodward, D.: Understanding Complexity: A Critique and Synthesis. Henley Management College, Henley on Thames, England (1991) Atmanspacher, H., Kurths, J., Scheingraber, H., Wackerbauer, R., Witt, A.: Complexity and Meaning in Nonlinear Dynamical Systems. Open systems and Information Dynamics 1, 269–289 (1991) Heylighen, F.: Self-Organization, Emergence and the Architecture of Complexity. In: AFCET (eds.) Proc. European Congress on System Science, Paris, pp. 23–32 (1992) Crutchfield, J.P.: Knowledge and Meaning... Chaos and Complexity. In: Lam, L., Naroditsky, V. (eds.) Modeling Complex Phenomena, pp. 66–101. Springer, Berlin (1992) Casti, J.L.: Reality Rules: Part I. Picturing the World in Mathematics: The Fundamentals, Part II. Picturing the World in Mathematics: The Frontier. J. Wiley and Sons, New-York (1992); The Simply Complex: Trendy Buzzword or Emerging New Science. Bull. of the Santa Fe Institute 7, 10–13 (1992) Badii, R.: Complexity and Unpredictable Scaling of Hierarchical Structures. In: Bountis, T. (ed.) Chaotic Dynamics, Theory and Practice, pp. 1–19. Plenum Press, New-York (1992) Kauffman, S.: At Home in the Universe: The Search for Laws of Self-Organization and Complexity. Oxford Univ. Press, New-York (1995) Auger, P.M.: Hierarchically Organized Systems The Response to Complexity. J. of Scientific and Industrial Research 51, 725–735 (1992) Ruthen, R.: Adapting to Complexity. Scientific American 268, 130–135 (1993) Kauffman, S.A.: The Origins of Order. Oxford Univ. Press, New-York (1993) Bates, J.E., Shepard, H.K.: Measuring Complexity Using Information Fluctuation. Phys. Letters A 172, 416–425 (1993) Holm, H.J.: Complexity in Economic Theory, University of Lund: Lund Economic Studies, Lund, Sweden (1993) Arthur, W.B.: Why Do Things Become More Complex? Scientific American 268, 92 (1993) Yates, F.E.: Order and Complexity in Dynamical Systems Homeodynamics as a Generalized Mechanics for Biology. Mathematical and Computer Modelling 19, 49–74 (1994) Ray, T.S.: Evolution, Complexity, Entropy and Artificial Reality. Physica D 75, 239–263 (1994); Evolution and Complexity. In: Cowan, G., Pines, D., Meltzer, D. (eds.) Complexity: Metaphors, Models and Reality, pp. 161–173. Addison Wesley, Reading (1994) Reggiani, A., Nijkamp, P.: Competition and Complexity in Spatially Connected Networks. System Dynamics Review 11, 51–66 (1995) Poon, L., Grebogi, C.: Controlling Complexity. Phys. Rev. Letters 75, 4023–4026 (1995) Horgan, J.: From Complexity to Perplexity. Scientific American 272, 74–79 (1995) Badii, R., Politi, A.: Complexity: Hierarchical Structures and Scaling in Physics. Cambridge Univ. Press, Cambridge (1997) Khalil, E.L.: Organizations, Naturalism and Complexity. Review of Social Economy 53, 393–419 (1995) Zeigarnik, A.V., Temkin, O.N.: A Graph Theoretic Model of Complex Reaction Mechanisms: a New Complexity Index for Reaction Mechanisms. Kinetics and Catalysis 37, 372–385 (1996) Helbing, D., Schweitzer, F. (Guest eds.): Complex Dynamics in Economics. Advances in Complex Systems 4(1), 1–176 (2001) Casti, J.L.: Connectivity, Complexity and Catastrophe in Large-Scale Systems. Intern. Ser. on Applied Systems Analysis, vol. 7. J. Wiley and Sons, Chichester (1979) Feldman, D.P., Crutchfield, J.P.: Measures of Statistical Complexity: Why? (November 11, 1997), Bennett, C.H.: How to Define Complexity in Physics and Why. In: Gregersen, N.H. (ed.) From Complexity To Life: On the Emergence of Life and Meaning. Oxford Univ. Press, New-York (2003) Lòpez-Ruiz, R., Mancini, H.L., Calbet, X.: A Statistical Measure of Complexity. Phys. Lett. A 209, 321–326 (1995) Feistel, R., Ebeling, W.: Evolution of Complex Systems: Self-Organization, Entropy and Development, Mathematics and its Applications. East European Series, vol. 30. Kluwer Acad. Publ., Dordrecht (1989) Frenken, K.: A Complexity Approach to Innovation Networks: The Case of the Aircraft Industry (1909-1997). Research Policy - A Journal Devoted to Research Policy, Research Management and Planning 29, 257–272 (2000) Lòpez Ruiz, R.: Shannon Information, LMC Complexity and Rényi Entropies: a Straightforward Approach (2003), Calbet, X., López-Ruiz, R.: Tendency towards Maximum Complexity in an Isolated Non-equilibrium System. Phys. Rev. E 60(9), 6–6116 (2001) Shiner, J.S., Davison, M., Landsberg, P.T.: Simple Measure for Complexity. Phys. Rev. E 59, 1459–1464 (1999) Crutchfield, J.P., Feldman, D.P., Shalizi, C.R.: Comment on Simple Measure for Complexity. Phys. Rev. E 62, 2559–2564 (2000) Shallit, J., Elsberry, W.: Playing Games with Probability: Dembski’s Complex Specified Information. In: Young, M., Edis, T. (eds.) Why Intelligent Design Fails: A Scientific Critique of the New Creationism, Piscataway, N.J (2004) Nicolis, G., Prigogine, I.: Exploring Complexity: an Introduction. W.H. Freeman and Co, New York (1989)
  8. 8.
    Albert, R., Barabasi, A.L.: Topology of Evolving Networks: Local Events and Universality. Phys. Rev. Letters 85, 5234–5237 (2000) Albert, R., Barabasi, A.L.: Statistical Mechanics of Complex Networks. Reviews of Modern Physics 74, 47–97 (2002) Albert, R., Jeong, H., Barabasi, A.L.: Diameter of the World Wide Web. Nature 401, 130–131 (1999) Albert, R., Jeong, H., Barabasi, A.L.: Error and Attack Tolerance of Complex Networks. Nature 406, 378–382, 409–542 (correction) (2000) Barabasi, A.L.: Linked: The New Science of Networks. Perseus Publishing, Cambridge (2002) Barabasi, A.L., Jeong, H., Néda, Z., Ravasz, E., Schubert, A., Vicsek, T.: Evolution of the Social Network of Scientific Collaborations. Physica A-311, 590–614 (2002) Bartholomay, A.F., Bianconi, G., Barabasi, A.L.: Competition and Multi-Scaling in Evolving Networks. Europhysics Letters 54, 436–442 (2001) Bartholomay, A.F., Bianconi, G., Barabasi, A.L.: Bose-Einstein Condensation in Complex Networks. Phys. Rev. Letters 86, 5632–5635 (2001) Bornholdt, S., Schuster, H.G. (eds.): Handbook of Graphs and Networks: From the Genome to the Internet. Wiley VCH Verlag, Weinheim (2003) Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph Structure in the Web. Computer Networks - the Intern. J. of Computer and Telecom. Networking 33, 309–320, See also special issue; Proc. 9th. Intern. World Wide Web Conference, the Web: the Next Generation, Amsterdam, May 15-19 (2000); Computer Networks - the Intern. J. of Computer and Telecom. Networking 33(1-6), v-viii, 1-843 (2001) Buchanan, M.: Nexus: Small Worlds and the Groundbreaking Science of Networks. W. W. Norton and Company, New-York (2002) Dorogovtsev, S.N., Mendes, J.F.F., Samukhin, A.N.: Principles of Statistical Mechanics of Uncorrelated Random Networks. Nucl. Phys. B 666, 396–416 (2003) Brossel, B., McKane, A.J.: Modelling Food Webs. In: Bornholdt, S., Schuster, H.G. (eds.) Handbook of Graphs and Networks: From the Genome to the Internet, pp. 218–247. Wiley VCH Verlag, Weinheim (2003) Ebeling, W., Sonntag, I., Schimansky-Geier, L.: On the Evolution of Biological Macromolecules II: Catalytic Networks. Studia Biophysica 84, 87–88 (1981) Erdös, P., Rényi, A.: On Random Graphs. I. Publicationes Mathematicae (Debrecen) 6, 290–297 (1959-1960); On the Evolution of Random Graphs. Publications of the Math. Institute of the Hungarian Academy of Sciences 5, 17–61 (1959-1960) Faloutsos, M., Faloutsos, P., Faloutsos, C.: On Power-Law Relationships of the Internet Topology. Computer Communications Review 29, 251–262 (1999) Sonntag, H.I.: Analysis of the Selection Equations for a Multivariable Population Model: Deterministic and Stochastic Solutions and Discussion of the Approach for Populations of Self-Reproducing Biochemical Networks. J. Theoretical Biology 93, 325–361 (1981) Huberman, B.A.: The Laws of the Web: Patterns in the Ecology of Information. The MIT Press, Cambridge (2001) Jain, S., Krishna, S.: A Model for the Emergence of Cooperation, Interdependence and Structure in Evolving Networks. Proc. National Acad. Sciences of the U.S.A. 98, 543–547 (2001) Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., Barabasi, A.L.: The Large-Scale Organization of Metabolic Networks. Nature 407, 651–654 (2000) Kirman, A.: Economic Networks. In: Bornholdt, S., Schuster, H.G. (eds.) Handbook of Graphs and Networks: From the Genome to the Internet, pp. 273–294. Wiley-VCH Verlag, Weinheim (2003) Klimontovich, Y.L.: Statistical Theory of Open Systems. In: Part 1: A Unified Approach to Kinetic Description of Processes in Active Systems. Fundamental Theories of Physics, vol. 67. Kluwer Acad. Publishers, Dordrecht (1995) Leydesdorff, L.: A Sociological Theory of Communication: The Self Organization of the Knowledge Based Society, 2nd edn. Universal Publishers, Parkland (2003) Maurer, S.M., Huberman, B.A.: Competitive Dynamics of Web Sites. J. Economic Dynamics and Control 27, 2195–2206 (2000) Juillard, M. Marcet, A. (guest eds.): Special issue, Computing in Economics and Finance. In: Proc. 6th Intern. Conf. of the Society for Computational Economics, Barcelona, Spain, July 6-8; J. Economic Dynamics and Control 27(11-12), 1939–2265 (2000) Milgram, S.: The Small World Problem. Psychology Today 1, 60–67 (1967) Montoya, J.M., Solé, R.V.: Small World Patterns in Food Webs. J. Theoretical Biology 214, 405–412 (2002) Nachtigall, C.: Selbstorganisation und Gewalt. Internationale Hochschulschriften, vol. 259. Waxmann Verlag, New York (1998) Newman, M.E.J.: Scientific Collaboration Networks: Part I. Network Construction and Fundamental Results. Phys. Rev. E 64, 016132, 8 (2001); Part II. Shortest Paths, Weighted Networks, and Centrality. Phys. Rev. E 64, 016132, 7 (2001) Newman, M.E.J.: Models of the Small World. J. Statistical Physics 101, 819–841 (2000) Newman, M.E.J., Watts, D.J.: Scaling and Percolation in the Small-World Network Model. Phys. Rev. E 60, 7332–7342 (1999) Pyka, A., Küppers, G. (eds.): Innovation Networks: Theory and Practice. New Horizons in the Economics of Innovation Series. Edward Elgar Publ., Cheltenham (2002) Rechenberg, I.: Evolutionsstrategie 1994, Werkstatt Bionik und Evolutionstechnik, vol. 1. Frommann-Holzboog-Verlag, Bad Cannstatt (1994) Scharnhorst, A.: Complex Networks and the Web: Insights from Nonlinear Physics. J. Computer Mediated Communication 8(4) (2003), Schwefel, H.P., Ebeling, W., Rosé, H., Weiss, O.: Optimization of Road Networks Using Evolutionary Strategies. Evolutionary Computation 5, 419–438 (1997) Scott, J.: Social Network Analysis: A Handbook, 2nd edn. SAGE Publ., London (2000) Solé, R.V., Montoya, J.M.: Complexity and Fragility in Ecological Networks. Proc. Royal Society London, Series B - Biological Sciences 268, 2039–2045 (2001) Sonntag, I.: Random Networks of Catalytic Biochemical Reactions. Biometrical J. 26, 799–807 (1984); Application of the Percolation Theory to Random Networks of Biochemical Reactions. IBID, 809–813 (1984) Sonntag, I., Feistel, R., Ebeling, W.: Random Networks of Catalytic Biochemical Reactions. Biometrical J. 23, 501–515 (1981) Strogatz, S.H.: Exploring Complex Networks. Nature 410, 268–276 (2001) Temkin, O.N., Zeigarnik, A.V., Bonchev, D.: Chemical Reaction Networks: A Graph Theoretical Approach. CRC Press, Boca Raton (1996) Wagner, A., Fell, D.: The Small World Inside Large Metabolic Networks. Proc Royal Society London, Series B - Biological Sciences 268, 1803–1810 (2000) Watts, D.J.: Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton Studies in Complexity. Princeton Univ. Press, Princeton (1999) Watts, D.J., Strogatz, S.H.: Collective Dynamics of ’Small World’ Networks. Nature 393, 440–442 (1998) Armbruster, D., Kaneko, K., Mikhailov, A.S.: Networks of Interacting Machines, Singapore. World Scientific Lecture Notes in Complex Systems, vol. 3 (2005) Google Scholar
  9. 9.
    McShea, D.: Metazoan Complexity and Evolution: is There a Trend? Evolution 50, 477–492 (1996) Saunders, P.T., Ho, M.W.: On the Increase of Complexity in Evolution. J. Theoretical Biology 90, 515–530 (1981) Goodwin, B.: How the Leopard Changed Its Spots. In: The Evolution of Complexity. Weidenfield and Nicholson, London (1994) Edmonds, B.: What is Complexity? the Philosophy of Complexity perse with Application to Some Examples in Evolution. In: Heylighen, F., Aerts (eds.) The Evolution of Complexity. Kluwer, Dordrecht (1994) Steward, R.: Self Organization in Evolution: a Mathematical Perspective. Phil. Trans. Royal Soc., London A361, 1101–1123 (2003) Gregersen, N.H. (ed.): From Complexity to Life: On the Emergence of Life and Meaning. Oxford Univ. Press, New-York (2003) Heylighen, F.: The Growth of Structural and Functional Complexity during Evolution. In: The Evolution of Complexity. Kluwer Acad. Publ., Dordrecht (1996) Ebeling, W., Jimenez Montano, M.A.: On Grammars, Complexity and Information Measures of Biological Macromolecules. J. Math. Bioscience 52, 3–71 (1980) Cohen, B., Harwood, W.T., Jackson, M.I.: The Specification of Complex Systems. Addison Wesley, New-York (1986) Flood, R.L., Carson, E.R.: Dealing with Complexity, 2nd edn. Plenum Press, New York (1993) Puri, S., Datta, S.: Nonlinearities in Complex Systems. Norosa Publ. House, Indian Institute of Advanced Studies (1997) Google Scholar
  10. 10.
    Prigogine, I.: Introduction to Thermodynamics of Irreversible Processes. American Lecture Series, vol. 185. Ch.C. Thomas Publisher, Springfield, 3rd edn., Interscience Publ. New-York (1967) Prigogine, I., Nicolis, G.: Self Organization in Non Equilibrium Systems: From Dissipative Structures to Order through Fluctuations. J. Wiley and Sons, New-York (1977) Klimontovitch, Y.L.: Theory of Open Systems. Kluwer, Dordrecht (1995) Kleidon, A., Lorenz, R.D. (eds.): Non-equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and beyond. Springer, Heidelberg (2005) Google Scholar
  11. 11.
    Kadomtsev, B.B.: Self Organization and Transport in Tokamak Plasma. Plasma Phys. and Nucl. Fus. 34(13), 1931–1938 (1992) Bautay, P., Janosi, I.M.: Self Organization and Anomalous Diffusion. Physica A 185(1-4), 11–18 (1992) Biebricher, C.K., Nicolis, G., Schuster, P.: Self-Organization in the Physico-Chemical and Life Sciences, Vol. 16546, EU Report, Brussels (1995) Schweitzer, F.: Multi-Agent Approach to the Self- Organization of Networks. In: Reed-Tsochas, F., Johnson, N.F., Efstathiou, J. (eds.) Understanding and Managing Complex Agent-Based Dynamical Networks. World Scientific, Singapore (2007) Ebeling, W., Schweitzer, F.: Self-Organization, Active Brownian Dynamics, and Biological Applications. Nova Acta Leopoldina NF 88(332), 169–188 (2003) Google Scholar
  12. 12.
    Strand, P.I.: Predictive Simulations of Transport in Tokamaks, PhD Thesis, Dept. of Electromagnetics, Chalmers Univ. of Technology (1999) Perkins, F., et al.: Nondimensional Transport Scaling in the Tokamak Fusion Test Reactor: is Tokamak Transport Bohm or Gyro Bohm? Phys. Fluids B 5, 422–498 (1998) Redd, A.J., Kritz, A.H., Bateman, G., Kinsey, J.E.: Sensitivity of Predictive Tokamak Plasma Transport Simulations. Phys. of Plasmas 4, 2207–2214 (1997) Google Scholar
  13. 13.
    Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence. Springer, New York (1992) Farge, M., Schneider, K., Pellegrino, G., Wray, A.A., Rogallo, R.S.: Coherent Vortex Extraction in 3D Homogeneous Turbulence: Comparison between CVS-wavelet and POD-Fourier Decompositions. Phys. Fluids 15(10), 2886–2896 (2003) Temam, R.: The Navier-Stokes Equations. North Holland, Amsterdam (1978) Klimontovich, Y.L.: Turbulent Motion and Structure of Chaos. Kluwer, Dordrecht (1991) Frisch, U.: Turbulence. Cambridge Univ. Press, Mass (1995) Nikolaenko, B., Foias, C., Temam, R.: The Connection between Infinite Dimensional and Finite Dimensional Dynamical Systems, AMS, Providence, RI (1992) Google Scholar
  14. 14.
    Cotsaftis, M.: Lectures on Advanced Dynamics, Taiwan Univ., Taipeh, R.O.C (1993) Google Scholar
  15. 15.
    Standish, R.K.: On Complexity and Emergence. Complexity International 9, 1–6 (2004) Fromm, J.: The Emergence of Complexity. Kassel Univ. Press (2004) Schweitzer, F.: Self Organization of Complex Structures: From Individual to Collective Dynamics. Gordon and Breach Science Publ., Amsterdam (1997) Johnson, S.: Emergence. Penguin Books, New-York (2001) Bedau, M.A.: Weak Emergence. In: Tomberlin, J. (ed.) Philosophical Perspectives: Mind, Causation, and World, vol. 11, pp. 375–399. Blackwell, Malden (1997) Strogatz, S.: Sync: The Emerging Science of Spontaneous Order. In: Hales, D., et al. (eds.) MABS 2003. LNCS (LNAI), vol. 2927. Springer, Heidelberg (2003) Ferber, J., Gutknecht, O., Michel, F.: From Agents To Organizations: An Organizational View of Multi Agent Systems. In: Giorgini, P., Müller, J.P., Odell, J.J., et al. (eds.) AOSE 2003. LNCS, vol. 2935, pp. 214–230. Springer, Heidelberg (2004) Bernon, C., Gleizes, M.-P., Peyruqueou, S., Picard, G.: ADELFE, a Methodology for Adaptive Multi-Agent Systems Engineering. In: Petta, P., Tolksdorf, R., Zambonelli, F., et al. (eds.) ESAW 2002. LNCS, vol. 2577, pp. 156–169. Springer, Heidelberg (2003) Fromm, J.: Types and Forms of Emergence, Bresciani, P., Perini, A., Giorgini, P., Giunchiglia, F., Mylopoulos, J.: A Knowledge Level Software Engineering Methodology for Agent Oriented Programming. In: ESAW 2002, pp. 648–655. ACM Press, New York (2001) Lind, J.: Iterative Software Engineering for Multiagent Systems. LNCS, vol. 1994, pp. 648–655. Springer, Heidelberg (2001) Jennings, N.: On Agent Based Software Engineering. Artificial Intelligence 117(2), 277–296 (2000) Kephart, J.O.: Research Challenges of Autonomic Computing. In: Proc. ICSE 2005, pp. 15–22 (2005) Kolp, M., Giorgini, P., Mylopoulos, J.: A Goal Based Organizational Perspective on Multi-Agent Architectures. In: Meyer, J.-J.C., Tambe, M. (eds.) ATAL 2001. LNCS (LNAI), vol. 2333, pp. 128–140. Springer, Heidelberg (2002) Maes, P.: Modelling Adaptive Autonomous Agents, Sycara, K.P.: Multi Agent Systems. AI Magazine 19(2), 79–92 (1998) Abbott, R.: Emergence Explained (to be published), Yamins, D.: Towards a Theory of ”Local to Global” in Distributed Multi-Agent Systems. In: Proc. Intern. Joint Conf. on Autonomous Agents and Multi Agent Systems (AAMAS 2005) (2005) Vogels, W., van Renesse, R., Birman, K.: The Power of Epidemics: Robust Communication for Large Scale Distributed Systems. ACM SIGCOMM Computer Communication Review 33(1), 131–135 (2003) Zambonelli, F., Jennings, N.R., Wooldridge, M.: Developing Multi Agent Systems: The Gaia Methodology. ACM Trans. on Software Engineering and Methodology 12(3), 317–370 (2003)
  16. 16.
    Schimansky Geier, L., Pöschel, T. (eds.): Stochastic Dynamics. Springer, Berlin (1997); Doob, J.: Stochastic Processes. J. Wiley and Sons, New York (1953) Gross, D.H.E.: Micro Canonical Thermodynamics. World Scientific, Singapore (2001) Zubarev, D.N., Röpke, G., Morozov, A.A.: Statistical Mechanics of Non Equilibrium Processes, vol. I & II, IBID. V.C.H. Viley, Weinheim (1996/1997) Yulmetyev, R., Hänggi, P., Gafarov, F.: Statistical Theory of Non Stationary Time Correlation in Complex Systems with Discrete Time. Nonlinear Phenomena in Complex Systems 5(2), 129–136 (2002) Google Scholar
  17. 17.
    Arnold, V.I., Avez, A.: Ergodic Problems of Classical Mechanics. Advanced Book Classics. Addison Wesley, Reading (1989) Jones, R.L., Ostrovskii, I., Rosenblatt, J.: Square Functions in Ergodic Theory. Ergodic Theory Dynamical Systems 16, 267–305 (1996) Kachurovskii, A.G.: The Rate of Convergence in Ergodic Theorems. Russian Math. Surveys 51(4), 653–703 (1996) Sinaï, Y.G.: Introduction to Ergodic Theory. Princeton Univ. Press, Princeton (1976) Cornfeld, I.P., Fomin, S.V., Sinai, Y.G.: Ergodic Theory. Springer, Berlin (1982) Petersen, K.: Ergodic Theory. Cambridge Studies in Advanced Math. Cambridge Univ. Press, Cambridge (1983) Pesin, Y., Barreira, L.: Lyapounov Exponents and Smooth Ergodic Theory. University Lecture Series no 23. American Math. Soc., Providence (2001) Bedford, T., Keane, M. (eds.): Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces. Oxford Univ. Press, Oxford (1991) Ollagnier, J.M.: Ergodic Theory and Statistical Mechanics. Lecture Notes in Math. No 1115. Springer, Berlin (1985) Lebowitz, J., Penrose, O.: Modern Ergodic Theory. Phys. Today 26, 155–175 (1973) Ruelle, D.: Ergodic Theory of Differentiable Dynamical Systems. Public. Mathématiques IHES 50, 27–58 (1979) Pugh, C., Shub, M.: Stable Ergodicity. Bull. Amer. Math. Soc. 41, 1–41 (2004) Mackey, G.W.: Ergodic Theory and its Significance for Statistical Mechanics and Probability Theory. Advances in Mathematics 12(2), 178–268 (1974) Birkhoff, G.D.: Proof of the Ergodic Theorem. Proc. National Acad. Sc. USA 17, 656–660 (1931) Kac, M.: Probability and Related Topics in Physical Science. Lectures in Applied Math. Series, vol. 1a. Amer. Math. Soc. (1957) Penrose, O.: Foundations of Statistical Mechanics. Rept. Progress Physics 42, 1937–2006 (1979) Google Scholar
  18. 18.
    Camazine, S., Deneubourg, J.L., Franks, N.R., Sneyd, J., Theraulaz, G., Bonabeau, E.: Self Organization in Biological Systems. Princeton Univ. Press, Princeton (2002) Shen, W.-M., et al.: Hormone Inspired Self Organization and Distributed Control of Robotic Swarms. Autonomous Robots 17, 93–105 (2004) Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: from Natural to Artificial Systems. Oxford Univ. Press, New-York (1999) Google Scholar
  19. 19.
    Eigen, M.: The Self-Organization of Matter and the Evolution of Biological Macromolecules. Die Natur-wissenschaften 58, 465–523 (1971) Eigen, M., Schuster, P.: The Hypercycle: A Principle of Natural Self-Organization. Part A: Emergence of the Hypercycle. Die Naturwissenschaften 64, 541–565 (1977) and Part C. The Realistic Hypercycle. IBID, 65, 341–369 (1978) Yates, F.E. (ed.): Self Organizing Systems: The Emergence of Order. Plenum Press (1987) Lewin, R.: Complexity Life at the Edge of Chaos. MacMillan, Basingstoke (1993) Lerner, A.Y. (ed.): Principles of Self Organization. Mir, Moscow (1966) Nolfi, S., Floreano, D.: Evolutionary Robotics: the Biology, Intelligence and Technology of Self-Organizing Machines. The MIT Press, Cambridge (2000) Serra, R., Andretta, M., Compiani, M., Zanarini, G.: Introduction to the Physics of Complex Systems (the Mesoscopic Approach to Fluctuations, Nonlinearity and Self-Organization). Pergamon Press, Oxford (1986) Google Scholar
  20. 20.
    Weidlich, W.: Socio-Dynamics: A Systematic Approach to Mathematical Modelling in the Social Sciences. Harwood Academic Publishers, Amsterdam (2000) Weidlich, W., Haag, G.: Concepts and Models of Quantitative Sociology: The Dynamics of Interacting Populations. Springer Series in Synergetics, vol. 14. Springer, Heidelberg (1983) Wolfram, S.: A New Kind of Science. Wolfram Media (2002) Bohm, D., Hiley, B.J.: The Undivided Universe. Routledge, New-York (1993) Bellouquid, A., Delitala, M.: Mathematical Modelling of Complex Biological Systems - a Kinetic Theory Approach. Birkhauser, Boston (2006) Google Scholar
  21. 21.
    Chandrasekhar, S.: Stochastic Problems in Physics and Astronomy. Rev. Mod. Phys. 15(1), 1–89 (1943) Risken, H.: The Fokker-Planck Equation, 2nd edn. Springer, Berlin (1996)Google Scholar
  22. 22.
    Cotsaftis, M.: A Passage to Complex Systems. In: Proc. CoSSoM 2006, Toulouse, France, September 24-27, 2006. Springer Series Understanding Complex Systems, Emergent Properties in Natural and Artificial Dynamical Systems (2006) Google Scholar
  23. 23.
    Salamon, D.: The Kolmogorov-Arnold-Moser Theorem, Preprint, ETH-Zürich (1986) Salamon, D., Zehnder, E.: KAM Theory in Configuration Space. Comment. Math. Helv. 64, 84–132 (1989) Sevryuk, M.: KAM-Stable Hamiltonians. J. Dyn. Control Syst. 1, 351–366 (1995) Pöschel, J.: A Lecture on the Classical KAM Theorem. In: Proc. Symp. Pure Math., vol. 69, pp. 707–732 (2000) Hamilton, R.S.: The Inverse Function Theorem of Nash-Moser. Bull. A.M.S. 7, 65–222 (1982) Alinhac, S., Gerard, P.: Opérateurs Pseudo-Différentiels et Thèoreme de Nash-Moser, Inter-Edition et Edition du CNRS (1991) Arnold, V.I.: Mathematical Methods of Classical Mechanics, 2nd edn. Springer, Heidelberg (1989) Arnold, V.I.: Dynamical Systems. Encyclopaedia of Math. Sci, vol. 3. Springer, Heidelberg (1988) Moser, J.: On Invariant Curves of Area Preserving Mappings of an Annulus. Nachr. Akad. Wiss. Gött, Math. Phys. Kl, pp. 1–20 (1962) Markus, L., Meyer, K.: Generic Hamiltonian Systems are neither Integrable nor Ergodic. Mem. Am. Math. Soc. 144 (1974) Moser, J.: Convergent Series Expansions for Quasi-periodic Motions. Math. Ann. 169, 136–176 (1967) Moser, J.: Stable and Random Motions in Dynamical Systems. Princeton Univ. Press, Princeton (1973); Zehnder, E.: Lectures on Hamiltonian Systems, Lecture Notes, ITCP (1973) Google Scholar
  24. 24.
    Tabor, M.: Chaos and Integrability in Nonlinear Dynamics, an Introduction. Wiley and Sons, New-York (1989) Stewart, I.: Does God Play Dice? The New Mathematics of Chaos. Penguin, Harmondsworth (1997) Abraham, N.B., Albano, A.M., Tufillaro, N.B.: Complexity and Chaos. In: Abraham, N.B. (ed.) Measures of Complexity and Chaos, pp. 1–25. Plenum Press, New Jersey (1989) Alliwood, K.T., Sauer, T.D., Yorke, J.A.: Chaos. An Introduction to Dynamical Systems. Springer, New York (1997) Moon, F.C.: Chaotic Vibrations. Wiley Interscience, New York (1987) Ott, E.: Chaos in Dynamical Systems. Cambridge Univ. Press, Cambridge (1993) Hilborn, R.C.: Chaos and Nonlinear Dynamics. Oxford Univ. Press, Oxford (1994) Prigogine, I.: Les Lois du Chaos, Nouvelle Bibliothéque Scientifique, Flammarion, Paris (1993) Chen, G.: Controlling Chaos and Bifurcations in Engineering Systems. CRC Press, Boca Raton (2000) Wiggins, S.: Chaotic Transport in Dynamical Systems. Springer, New York (1991) Strogatz, S.H.: Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering. Addison-Wesley, Reading (1994) Strogatz, S.H.: Sync: The Emerging Science of Spontaneous Order, Theia (2003) Cvitanovic, P.: Universality in Chaos. Adam Hilger, Bristol (1984); Hilborn, R.C.: Chaos and Nonlinear Dynamics. Oxford Univ. Press, Oxford (1994) Magnitskii, N.A., Vasilevich, S.V.: New Methods for Chaotic Dynamics, Singapore. World Scientific Series on Nonlinear Science, Ser. A (2006) Kapitaniak, T.: Chaos for Engineers: Theory, Applications and Control. Springer, Berlin (1998) Sagdeev, R.Z., Usikov, D.A., Zaslavsky, G.M.: Nonlinear Physics; from Pendulum to Turbulence and Chaos. Harwood Academic, New York (1988) Google Scholar
  25. 25.
    Poincaré, H.: Les Méthodes Nouvelles de la Mécanique Céleste, Gauthier Villars, Paris, vol. 3 (1892-1999) Arnold, V.I.: Small Denominators and Problems of Stability of motion in Classical and Celestial Mechanics. Russian Math. Surveys 18(6), 85–191 (1963) Arnold, V.I.: Mathematical Methods of Classical Mechanics. Springer, New York (1978) Arnold, V.I., Koslov, V.V., Neishtadt, A.I.: Dynamic Systems III: Mathematical Aspects of Classical and Celestial Mechanics. Springer, Berlin (1993) Bambusi, D.: Nekhoroshev Theorem for Small Amplitude Solutions in Nonlinear Schrdinger Equations. Math. Zb. 230(2), 345–387 (1999) Benettin, G., Gallavotti, G.: Stability of Motion near Resonances in Quasi Integrable Hamiltonian Systems. J. of Statistical Physics 44(3-4), 293–338 (1986) Bierstone, E., Milman, P.D.: Semi Analytic and Sub Analytic Sets. Publ. Math. IHES 67, 5–42 (1988) Broer, H.W., Huitema, G.B., Sevryuk, M.B.: Quasi Periodicity in Families of Dynamical Systems: Order amidst Chaos. LNM, vol. 1645, pp. 5–42. Springer, New York (1996) Katok, A., Hasselblatt, B.: Introduction to the Modern Theory of Dynamical Systems. Cambridge Univ. Press, Mass (1996) Bogoliubov, N.N., Mitropolskii, Y.A., Samoilenko, A.M.: Methods of Accelerated Convergence in Nonlinear Mechanics. Springer, Berlin (1976) Google Scholar
  26. 26.
    Hirsch, M., Pugh, C., Shub, M.: Invariant Manifolds. Lecture Notes in Math, vol. 583. Springer, Berlin (1977) Tabor, M.: Chaos and Integrability in Nonlinear Dynamics, an Introduction. Wiley and Sons, New-York (1989) Goriely, A.: Integrability and non Integrability of Dynamical Systems. World Scientific Publ., Singapore (2001)Google Scholar
  27. 27.
    Lefschetz, S.: Stability of Nonlinear Control Systems. Academic Press, New-York (1965) Aizerman, M.A., Gantmacher, F.R.: Absolute Stability of Regulator Systems. Holden Day, San Franscisco (1964) Dullerud, G.E., Paganini, F.: A Course in Robust Control Theory: a Convex Approach. Springer, New York (2000) Hsu, J.C.S., Meyer, A.U.: Modern Control Principles and Applications. McGraw Hill, New-York (1968) Arimoto, S.: Control Theory of Nonlinear Mechanical Systems: a Passivity Based and Circuit Theoretic Approach. Oxford Univ. Press, Oxford (1996) Russell, S., Norvig, P.: Artificial Intelligence: a Modern Approach. Prentice Hall, Englewood Cliffs (1995) Burl, J.H.: Linear Optimal Control, H2 and H ∞  Methods. Addison-Wesley Longman, Menlo Park (1999) Leonov, G.A., Ponomarenko, I.V., Smirnova, V.B.: Frequency Domain Methods for Nonlinear Analysis: Theory and Applications. World Scientific Publ., Singapore (1996) Astrom, K.J.: Control of Complex Systems. Springer, Berlin (2000) Antsaklis, P.J., Passino, K.M.: An Introduction to Intelligent and Autonomous Control. Kluwer Acad. Publ., Norwell (1993) Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Prentice Hall, Englewood Cliffs (1994) Yudin, D., Goryashko, A.: Control Problems and Complexity Theory, Part I. Engineering Cybernetics (USSR) 12, 10–24 (1974); Part II, IBID, 13, 1–13 (1975) Morris, K.A.: Design of Finite-dimensional Controllers for Infinite-dimensional Systems by Approximation. J. Mathematical Systems, Estimation and Control 4(2), 1–30 (1994) Brown, M., Harris, C.: Neuro Fuzzy Adaptive Modelling and Control. Prentice Hall, Englewood Cliffs (1994) Kosko, B.: Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence. Prentice Hall, Englewood Cliffs (1991) Grigorenko, I.: Optimal Control and Forecasting of Complex Dynamical Systems. World Scientific, Singapore (2006) Byrnes, C.I., Martin, C.F., Saeks, R.E. (eds.): Analysis and Control of Nonlinear Systems. North-Holland, Amsterdam (1988) Conte, G., Moog, C.H., Perdon, A.M.: Nonlinear Control Systems - An Algebraic Setting. Springer, London (1998) Ng, G.W.: Application of Neural Networks to Adaptive Control of Nonlinear Systems. Research Studies Press, London (1997) Francis, B.A.: A Course in H ∞  Control Theory. Springer, Berlin (1987); Dorf, R.C., Bishop, R.H.: Modern Control Systems. Addison Wesley, Reading (1995) Helton, J.W., James, M.R.: Extending H ∞  Control to Nonlinear Systems. Frontiers in Appl. Sci. SIAM, Philadelphia (1999) Ionescu, V., Stoica, A.: Robust Stabilization and H ∞  Problems. Kluwer Acad. Publ., Dordrecht (1999) Emelyanov, S.V., Burovoi, A., Levada, F.Y.: Control of Indefinite Nonlinear Dynamic Systems: Induced Internal Feedback. Springer, London (1998) Dullerud, G.E., Paganini, F.: A Course in Robust Control Theory: A Convex Approach. Springer, New York (2000) Fradkov, A.L., Miroshnik, I.V., Nikiforov, V.O.: Nonlinear and Adaptive Control of Complex Systems. Kluwer Acad. Publ., Dordrecht (1999) Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Nonlinear and Adaptive Control Design. J. Wiley and Sons, New York (1995) Francis, B.A., Tanenbaum, A.R. (eds.): Feedback Control, Nonlinear Systems and Complexity. Springer, New York (1995) Schroeder, D. (ed.): Intelligent Observer and Control Design for Nonlinear Systems. Springer, New York (2000) Solodovnikov, V.V., Tumarkin, V.I.: Complexity Theory and the Design of Control Systems, Theory and Methods of Systems Analysis, vol. 28, Nauka, Moscow (1990) Wang, H.O., Tanaka, K., Griffin, F.: An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues. IEEE Trans. On Fuzzy Systems 4(1), 14–23 (1996) Gopal, M.: Modern Control System Theory, 2nd edn. J. Wiley and Sons, Toronto (1993) Wang, L.X.: Adaptive Fuzzy Systems and Control. Prentice Hall, Englewood Cliffs (1994) Google Scholar
  28. 28.
    Deimling, K.: Nonlinear Functional Analysis. Springer, Berlin (1985) Krasnoselskii, M.A.: Asymptotics of Nonlinearities and Operator Equations. Birkhäuser, Boston (1995) Schwartz, J.: Nonlinear Functional Analysis. Gordon and Breach, New York (1969) Vainberg, M.M.: Variational Methods for the Study of Nonlinear Operators. Holden Day, San Francisco (1964) Zeidler, E.: Nonlinear Functional Analysis and its Applications, vol. I-III-IV. Springer, New York (1985-1986-1988) Bendat, J.S.: Nonlinear Systems Techniques and Applications. J. Wiley and Sons, New York (1998) Bobylev, N.A., Burman, Y.M., Korovin, S.K.: Nonlinear Analysis and Applications. Walter de Gruyter, Berlin (1994) Bogaesvski, V.N., Povzner, A.: Algebraic Methods in Nonlinear Perturbation Theory. Springer, New York (1991) Lusternik, L.A., Sobolev, V.I.: Elements of Functional Analysis. Ungar, New York (1961) Hale, J.K., Verduyn Lunel, S.M.: Theory of Functional Differential Equations. Springer, New York (1993) Google Scholar
  29. 29.
    Corduneanu, C.: Almost Periodic Functions. Interscience Tracts in Pure and Applied Maths, vol. 22. Interscience, New-York (1961) Dubinskij, J.A.: Sobolev Spaces of Infinite Order and Differential Equations. Teubner, Leipzig (1988) Amerio, L., Prouse, G.: Almost Periodic Functions and Functional Equations. Van Nostrand-Reinhold, New-York (1971) Mazja, V.G.: Sobolev Spaces. Springer, New-York (1985) Rao, M.M., Ren, Z.D.: Theory of Orlicz Spaces. Marcel Dekker, New-York (1991) Google Scholar
  30. 30.
    Dugundji, J., Granas, A.: Fixed Point Theory, vol. I. Polish Scientific Publ., Warsaw (1982) Jiang, T.H.: Fixed Point Theory. Springer, New-York (1985) Zeidler, E.: Nonlinear Functional Analysis and its Applications. Springer, New-York (1986) Smart, D.R.: Fixed Point Theorems. Cambridge Univ. Press, Mass. (1980) Burton, T.A.: Stability by Fixed Point Theory for Functional Differential Equations. Dover Publ., New-York (2006) Google Scholar
  31. 31.
    Cotsaftis, M.: Recent Advances in Control of Complex Systems. In: Survey Lecture, Proc. ESDA 1996, Montpellier, France, ASME, vol. I, p. 1 (1996) Cotsaftis, M.: Comportement et Controle des Systemes Complexes. Diderot, Paris (1997) Cotsaftis, M.: Popov Criterion Revisited for Other Nonlinear Systems. In: Proc. ISIC 2003 (International Symposium on Intelligent Control), Houston, October 5-8 (2003) Google Scholar
  32. 32.
    Renouzenko, A.V.: Partial Differential Equations with Discrete and Distributed State Dependent Delays. J. Math. Anal. Applic. 326(2), 1031–1045 (2007) Google Scholar
  33. 33.
    Appell, J., Zabrijko, P.P.: Nonlinear Superposition Operators. Cambridge University Press, Mass. (1990) Google Scholar
  34. 34.
    Pachpatte, B.G.: Mathematical Inequalities. North Holland/Elsevier, Amsterdam (2005) Bainov, D., Simeonov, P.: Integral Inequalities and Applications. Kluwer Academic Press, Dordrecht (1992) Kim, Y.H.: Explicit Bounds on Some Nonlinear Integral Inequalities. J. Inequalities in Pure and Applied Mathematics 7(2) (2006) Mitrinovic, D.S., Pecaric, J.E., Fink, A.M.: Inequalities Involving Functions and Their Integrals and Derivatives. Kluwer Acad. Publ., Dordrecht (1991) Google Scholar
  35. 35.
    Cotsaftis, M.: Robust Asymptotically Stable Control for Intelligent Unknown Mechatronic Systems. In: Proc. ICARCV, Singapore, December 5-8 (2006) Google Scholar
  36. 36.
    Cotsaftis, M.: Beyond Mechatronics, Toward Global Machine Intelligence. In: Proc. ICMT 2005, Kuala-Lumpur, December 6-8 (2005) Google Scholar
  37. 37.
    Cotsaftis, M.: From Trajectory Control to Task Control - Emergence of Self Organization in Complex Systems. In: Aziz-Alaoui, M.A., Bertelle, C. (eds.) Emergent Properties in Natural and Artificial Dynamical Systems, pp. 3–22. Springer, Heidelberg (2006) Cotsaftis, M.: On the Definition of Task Oriented Intelligent Control. In: Proc. ISIC 2002 Conf., Vancouver, October 27-30 (2002) Google Scholar
  38. 38.
    Cotsaftis, M.: Merging Information Technologies with Mechatronics - The Autonomous Intelligence Challenge. In: Proc. IEECON 2006, Paris, November 6-10 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Michel Cotsaftis
    • 1
  1. 1.ECEParisFrance

Personalised recommendations