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
H. Haken, Advanced Synergetics, Springer Series in Synergetics, 20, Springer Verlag, Berlin, Heidelberg, New York (1983).
G. Nicolis, I. Prigogine, Self-Organization in Non-Equilibrium Systems, Wiley, New York (1977).
W. Ebeling, R. Feistel, Physik der Selbstorganisation und Evolution, Akademie-Verlag, Berlin (1982).
W. Ebeling, R. Feistel, Physik der Selbstorganisation und Evolution, Akademie-Verlag, Berlin (1986).
R. Feistel, W. Ebeling, Evolution of Complex Systems, Verlag d. Wissenschaften, Berlin (1989).
M. Eigen, P. Schuster, The Hypercycle, Naturwiss. 64, 541 (1977).
M. Eigen, P. Schuster, The Hypercycle, Naturwiss. 65, 341 (1978).
P. Schuster, Dynamics of Molecular Evolution, Physica 22D, 100 (1986).
W. Ebeling, M. Peschel (edits.), Cooperation and Competition in Dynamical Systems, A kademie-Verlag, Berlin (1985).
M.Peschel, W.Mende, The Predator-Prey Model: Do we live in a Volterra World?, Akademie-Verlag, Berlin (1986).
W. Ebeling, Chaos, Ordnung und Information, Urania-Verlag, Leipzig (1986).
M.V. Wolkenstein, Entropie und Information. Nauka, Moskva (1986) (in Russ.), Akademie-Verlag, Berlin (1989), ( German transl.).
H. Haken (Ed.), Complex Systems - Operational Approaches in Neurobiology, Physics and Computers, Springer Verlag, Berlin, Heidelberg, New York (1985).
H. Haken (Ed.), Computational Systems - Natural and Artificial, Springer-Verlag, Berlin, Heidelberg, New York (1987).
H. Haken (Ed.), Information and Self-Organization, Springer-Verlag, Berlin, Heidelberg (1988).
H. Haken, Der Computer erkennt mein Gesicht, Bild der Wiss. 8, 49 (1988), (in German).
J.S. Nicolis, Chaotic Dynamics Applied to Information Processing, Akademie-Verlag, Berlin (1987).
W.D. Hillis, The Connection Machine, Sci. American 256, (6), 86 (1987).
W. Ebeling, Physik komplexer nichtlinearer Netzwerke und neue Wege der Informationsverarbeitung, Sitzungsberichte der AdW der DDR, Akademie-Verlag, Berlin (1987).
T. Kohonen, An Introduction to Neural Computing, Neural Networks 1, 3 (1988).
S. Grossberg, Nonlinear Neural Networks. Neural Networks 1, 17 (1988).
J.J. Hopfield, Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proc. Natl. Acad. Sci. USA 78, 2554 (1982).
A. Engel. H. Englisch, A. Schütte, Improved Retrieval in Neural Networks with External Fields, Europhys. Lett. submitted.
Y.A. Vasilev, Yu.M. Romanovsky, D.S. Chernaysky and V.G. Yakhno, Autowave Processes in Kinetic Systems, Verl. d. Wiss., Berlin (1987).
M. Conrad, K.G. Kirby, Intraneuronal Dynamics as a Substrate for Evolutionary Learning, Physica 22D, 205 (1986).
M. Conrad, On Design Properties for Molecular Computers; Comm. of the ACM 28, 5 (1985).
F. Harary, R.Z. Norman, D. Cartwright, Structural Models, Wiley, New York (1985).
I. Sonntag, R. Feistel, W. Ebeling, Random Networks of Catalytic Biochemical Reactions, B iometr. J. 23, 91 (1981).
D.H. Ackley, G.E. Hinton, T.J. Sejnowski, A Learning Algorithm for Boltzmann Machines, Cogn. Sci. 9, 147 (1985).
W. Ebeling, Th. Boseniuk, Th. Pöschel, Simulation of Learning Networks, Proc. Parcella, Berlin (1988).
J.L. McClelland, D.E. Rumelhard (Eds.), Parallel Distributed Processing, MIT Press, Cambridge, Mass. (1986).
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).
J. Schnakenberg, Network Theory of Master Equation Systems, Rev. Mod. Phys. 48, (1976).
W. Ebeling, I. Sonntag, Stochastic Description of Evolutionary Processes in Underoccupied Systems, BioSystems 19, 91 (1986).
H. Risken, The Fokker-Planck Equation, Springer Series in Synergetics 18, Springer-Verlag, Berlin, Heidelberg, New York (1984).
H. Malchow, L. Schimansky-Geier, Noise and Diffusion in Bistable Nonequilibrium Systems, Teubner-Texte zur Physik 5, Teubner-Verlagsgesellschaft, Leipzig (1985).
L. Schimansky-Geier, W. Ebeling, Stochastic Theory of Nucleation in Nonequilibrium Bistable Reaction Systems, Ann. Physik, Leipzig 40, 10 (1983).
J.J. Hopfield and D.W.Tank: Computing RC-Networks, Biol. Cybern. 52, 141 (1985).
W. Ebeling, Pattern Processing and Optimization by Reaction Diffusion Systems, J. Stat. Phys. 45, (5/6), 891 (1986).
Cellular Automata, Proc. of an Intern. Workshop, Los Alamos NM in Physica 10D, (1984).
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer Series in Synergetics 19, Springer-Verlag, Berlin, Heidelberg, New York (1984).
H. Haken, Model of a Chemical Parallel Computer for Pattern Recognition and Associative Memory, J. de Chimie physique 84, (11/12), 1289 (1989).
B.N. Belintzev, M.A. Livshitz, M.V. Volkenstein, Selforganization as a Result of Effective Nonlinearity, Phys. Lett. 82A, (8), 20 (1981).
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.).
A.A. Kalnin, On Possible Distributed Recording of the Signals in Non-Equilibrium Cooperative Systems (Structural Reflexia), Biofizika 29, (1), 117 (1984).
A.A. Kalnin, On Possible Distributed Recording of the Signals in Non-Equilibrium Cooperative Systems (Structural Reflexia), Biofizika 29, (1), 117 (1984).
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).
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.
K. Kawasaki, T. Ohta, Kinetic Drummhead Model of Interface (1), Theor.Phys. 67, 147 (1982).
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).
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).
T. Toffoli, M. Margolus, Cellular Automata Machines, MIT Press, Cambridge Mass,, London England, (1987).
Ch. Zülicke, Formation of Spiral Waves from Inhomogeneous Initial Conditions, submitted to Z. Naturf.
N.A. Gorelova, and I. Bures, Spiral Waves of Spreading Depression in the Isolated Chicken Retina, J. Neurobiol. 6 (1983).
M.V. Volkenstein, Biophysics, Mir Publ. Moscow, (1983).
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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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