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Part of the book series: Springer Series in Synergetics ((SSSYN,volume 44))

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Abstract

The dynamics of networks is closely connected with the development of the modern science of non-linear irreversible processes [1–6].

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References

  1. H. Haken, Advanced Synergetics, Springer Series in Synergetics, 20, Springer Verlag, Berlin, Heidelberg, New York (1983).

    Google Scholar 

  2. G. Nicolis, I. Prigogine, Self-Organization in Non-Equilibrium Systems, Wiley, New York (1977).

    Google Scholar 

  3. W. Ebeling, R. Feistel, Physik der Selbstorganisation und Evolution, Akademie-Verlag, Berlin (1982).

    Google Scholar 

  4. W. Ebeling, R. Feistel, Physik der Selbstorganisation und Evolution, Akademie-Verlag, Berlin (1986).

    Google Scholar 

  5. R. Feistel, W. Ebeling, Evolution of Complex Systems, Verlag d. Wissenschaften, Berlin (1989).

    Google Scholar 

  6. M. Eigen, P. Schuster, The Hypercycle, Naturwiss. 64, 541 (1977).

    Article  CAS  Google Scholar 

  7. M. Eigen, P. Schuster, The Hypercycle, Naturwiss. 65, 341 (1978).

    Article  CAS  Google Scholar 

  8. P. Schuster, Dynamics of Molecular Evolution, Physica 22D, 100 (1986).

    Article  Google Scholar 

  9. W. Ebeling, M. Peschel (edits.), Cooperation and Competition in Dynamical Systems, A kademie-Verlag, Berlin (1985).

    Google Scholar 

  10. M.Peschel, W.Mende, The Predator-Prey Model: Do we live in a Volterra World?, Akademie-Verlag, Berlin (1986).

    Google Scholar 

  11. W. Ebeling, Chaos, Ordnung und Information, Urania-Verlag, Leipzig (1986).

    Google Scholar 

  12. M.V. Wolkenstein, Entropie und Information. Nauka, Moskva (1986) (in Russ.), Akademie-Verlag, Berlin (1989), ( German transl.).

    Google Scholar 

  13. H. Haken (Ed.), Complex Systems - Operational Approaches in Neurobiology, Physics and Computers, Springer Verlag, Berlin, Heidelberg, New York (1985).

    Google Scholar 

  14. H. Haken (Ed.), Computational Systems - Natural and Artificial, Springer-Verlag, Berlin, Heidelberg, New York (1987).

    Google Scholar 

  15. H. Haken (Ed.), Information and Self-Organization, Springer-Verlag, Berlin, Heidelberg (1988).

    Google Scholar 

  16. H. Haken, Der Computer erkennt mein Gesicht, Bild der Wiss. 8, 49 (1988), (in German).

    Google Scholar 

  17. J.S. Nicolis, Chaotic Dynamics Applied to Information Processing, Akademie-Verlag, Berlin (1987).

    Google Scholar 

  18. W.D. Hillis, The Connection Machine, Sci. American 256, (6), 86 (1987).

    Google Scholar 

  19. W. Ebeling, Physik komplexer nichtlinearer Netzwerke und neue Wege der Informationsverarbeitung, Sitzungsberichte der AdW der DDR, Akademie-Verlag, Berlin (1987).

    Google Scholar 

  20. T. Kohonen, An Introduction to Neural Computing, Neural Networks 1, 3 (1988).

    Article  Google Scholar 

  21. S. Grossberg, Nonlinear Neural Networks. Neural Networks 1, 17 (1988).

    Article  Google Scholar 

  22. J.J. Hopfield, Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proc. Natl. Acad. Sci. USA 78, 2554 (1982).

    Article  Google Scholar 

  23. A. Engel. H. Englisch, A. Schütte, Improved Retrieval in Neural Networks with External Fields, Europhys. Lett. submitted.

    Google Scholar 

  24. Y.A. Vasilev, Yu.M. Romanovsky, D.S. Chernaysky and V.G. Yakhno, Autowave Processes in Kinetic Systems, Verl. d. Wiss., Berlin (1987).

    Book  Google Scholar 

  25. M. Conrad, K.G. Kirby, Intraneuronal Dynamics as a Substrate for Evolutionary Learning, Physica 22D, 205 (1986).

    Article  Google Scholar 

  26. M. Conrad, On Design Properties for Molecular Computers; Comm. of the ACM 28, 5 (1985).

    Article  Google Scholar 

  27. F. Harary, R.Z. Norman, D. Cartwright, Structural Models, Wiley, New York (1985).

    Google Scholar 

  28. I. Sonntag, R. Feistel, W. Ebeling, Random Networks of Catalytic Biochemical Reactions, B iometr. J. 23, 91 (1981).

    Google Scholar 

  29. D.H. Ackley, G.E. Hinton, T.J. Sejnowski, A Learning Algorithm for Boltzmann Machines, Cogn. Sci. 9, 147 (1985).

    Google Scholar 

  30. W. Ebeling, Th. Boseniuk, Th. Pöschel, Simulation of Learning Networks, Proc. Parcella, Berlin (1988).

    Google Scholar 

  31. J.L. McClelland, D.E. Rumelhard (Eds.), Parallel Distributed Processing, MIT Press, Cambridge, Mass. (1986).

    Google Scholar 

  32. W. Ebeling, L. Schimansky-Geier, Transition Phenomena in Multi-Dimensional Systems - Models of Evolution, in: F. Moss, P. McClintock (Eds.), Noise in Nonlinear Dynamical Systems, Cambridge University Press, Cambridge, Mass. (1989).

    Google Scholar 

  33. J. Schnakenberg, Network Theory of Master Equation Systems, Rev. Mod. Phys. 48, (1976).

    Google Scholar 

  34. W. Ebeling, I. Sonntag, Stochastic Description of Evolutionary Processes in Underoccupied Systems, BioSystems 19, 91 (1986).

    Article  CAS  Google Scholar 

  35. H. Risken, The Fokker-Planck Equation, Springer Series in Synergetics 18, Springer-Verlag, Berlin, Heidelberg, New York (1984).

    Google Scholar 

  36. H. Malchow, L. Schimansky-Geier, Noise and Diffusion in Bistable Nonequilibrium Systems, Teubner-Texte zur Physik 5, Teubner-Verlagsgesellschaft, Leipzig (1985).

    Google Scholar 

  37. L. Schimansky-Geier, W. Ebeling, Stochastic Theory of Nucleation in Nonequilibrium Bistable Reaction Systems, Ann. Physik, Leipzig 40, 10 (1983).

    Article  CAS  Google Scholar 

  38. J.J. Hopfield and D.W.Tank: Computing RC-Networks, Biol. Cybern. 52, 141 (1985).

    CAS  Google Scholar 

  39. W. Ebeling, Pattern Processing and Optimization by Reaction Diffusion Systems, J. Stat. Phys. 45, (5/6), 891 (1986).

    Article  Google Scholar 

  40. Cellular Automata, Proc. of an Intern. Workshop, Los Alamos NM in Physica 10D, (1984).

    Google Scholar 

  41. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer Series in Synergetics 19, Springer-Verlag, Berlin, Heidelberg, New York (1984).

    Google Scholar 

  42. H. Haken, Model of a Chemical Parallel Computer for Pattern Recognition and Associative Memory, J. de Chimie physique 84, (11/12), 1289 (1989).

    Google Scholar 

  43. B.N. Belintzev, M.A. Livshitz, M.V. Volkenstein, Selforganization as a Result of Effective Nonlinearity, Phys. Lett. 82A, (8), 20 (1981).

    Google Scholar 

  44. S.A. Gerson, A.S. Mikhailov, Possible Mechanism for the Analysis of patterns by Non-Equilibrium Biochemical Systems, Dokl. Akad. Nauk. SSSR 291 (1) 228 (1986), (in Russ.).

    Google Scholar 

  45. A.A. Kalnin, On Possible Distributed Recording of the Signals in Non-Equilibrium Cooperative Systems (Structural Reflexia), Biofizika 29, (1), 117 (1984).

    Google Scholar 

  46. A.A. Kalnin, On Possible Distributed Recording of the Signals in Non-Equilibrium Cooperative Systems (Structural Reflexia), Biofizika 29, (1), 117 (1984).

    Google Scholar 

  47. L. Kuhnert, L. Pohlmann, H.-J. Krug, G. Wessler, Repressing of Chemical Waves by Photochemical Inhibitor Releasing, in: W. Ebeling, H. Ulbricht (Eds.), Selforganization by Nonlinear Irreversible processes, Springer Series in Synergetics 33, Springer-Verlag, Berlin, Heidelberg, New York (1986).

    Google Scholar 

  48. J.J. Tyson, A Quantitative Account of Oscillations, Bistability, and Traveling Waves in the BZR, in: M. Burger, R.J. Field (Eds.), Oscillations and Traveling Waves in Chemical Reactions, Wiley, New York (1985) p. 111.

    Google Scholar 

  49. K. Kawasaki, T. Ohta, Kinetic Drummhead Model of Interface (1), Theor.Phys. 67, 147 (1982).

    Article  CAS  Google Scholar 

  50. A. Engel, W. Ebeling, R. Feistel, L. Schimansky-Geier, Dynamics of Interfaces in Random Media, in: W. Ebeling, H. Ulbricht (Eds.), Selforganization by Nonlinear Irreversible Processes, Springer Series in Synergetics 33, Springer-Verlag, Berlin, Heidelberg, New York (1986).

    Google Scholar 

  51. N. Wiener, A. Rosenblueth, The Mathematical Formulation of the Problem of Conduction of Impulses in a Network of Connected Excitable Elements, Specifically in Cardiac Muscle, Arch. Inst. Cadiol. Mex. 16, 205 (1946).

    CAS  Google Scholar 

  52. T. Toffoli, M. Margolus, Cellular Automata Machines, MIT Press, Cambridge Mass,, London England, (1987).

    Google Scholar 

  53. Ch. Zülicke, Formation of Spiral Waves from Inhomogeneous Initial Conditions, submitted to Z. Naturf.

    Google Scholar 

  54. N.A. Gorelova, and I. Bures, Spiral Waves of Spreading Depression in the Isolated Chicken Retina, J. Neurobiol. 6 (1983).

    Google Scholar 

  55. M.V. Volkenstein, Biophysics, Mir Publ. Moscow, (1983).

    Google Scholar 

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Ebeling, W., Schimansky-Geier, I., Zülicke, C. (1989). Dynamics of Networks and Pattern Processing. In: Plath, P.J. (eds) Optimal Structures in Heterogeneous Reaction Systems. Springer Series in Synergetics, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83899-6_7

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  • DOI: https://doi.org/10.1007/978-3-642-83899-6_7

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