Stochastic Phenomena and Chaotic Behaviour in Complex Systems Proceedings of the Fourth Meeting of the UNESCO Working Group on Systems Analysis Flattnitz, Kärnten, Austria, June 6–10, 1983

This book contains all invited contributions of an interdisciplinary workshop of the UNESCO working group on systems analysis of the European and North American region entitled "Stochastic Phenomena and Chaotic Behaviour in Complex Systems". The meeting was held at Hotel Winterthalerhof in Flattnitz, Karnten, Austria from June 6-10, 1983. This workshop brought together some 20 mathematicians, physicists, chemists, biologists, psychologists and economists from different European and American coun­ tries who share a common interest in the dynamics of complex systems and their ana­ lysis by mathematical techniques. The workshop in Flattnitz continued a series of meetings of the UNESCO working group on systems analysis which started in 1977 in Bucharest and was continued in Cambridge, U.K., 1981 and in Lyon, 1982. The title of the meeting was chosen in order to focus on one of the current problems of the analysis of dynamical systems. A deeper understanding of the vari­ ous sources of stochasticity is of primary importance for the interpretation of experimental observations. Chaotic dynamics plays a central role since it intro­ duces a stochastic element into deterministic systems.

Introductory Remarks.- I General Concepts.- Some Basic Ideas on a Dynamic Information Theory.- Aspects of Optimization and Adaptation.- Relaxed Markov Processes, Jackson Networks and Polymerisation.- II Chaotic Dynamics-Theory.- Noodle-Map Chaos: A Simple Example.- A Mechanism for Spurious Solutions of Nonlinear Boundary Value Problems.- Approach to Equilibrium: Kuzmin’s Theorem for Dissipative and Expanding Maps.- Complex Behaviours in Macrosystems Near Polycritical Points.- III Chaotic Dynamics — Real Systems and Experimental Verification.- Chaos in Classical Mechanics: The Double Pendulum.- Chaos in Continuous Stirred Chemical Reactors.- The Interface Between Mathematical Chaos and Experimental Chemistry.- The Enzyme and the Strange Attractor—Comparisons of Experimental and Numerical Data for an Enzyme Reaction with Chaotic Motion.- Nonuniform Information Processing by Strange Attractors of Chaotic Maps and Flows.- IV Stability and Instability in Dynamical Networks.- Generalized Modes and Nonlinear Dynamical Systems.- Dynamics of Linear and Nonlinear Autocatalysis and Competition.- Permanence and Uninvadability for Deterministic Population Models.- V Stochasticity in Complex Systems.- Random Selection and the Neutral Theory—Sources of Stochasticity in Replication.- The Dynamics of Catalytic Hypercycles—A Stochastic Simulation.- Perturbation-Dependent Coexistence and Species Diversity in Ecosystems.- Chance and Necessity in Urban Systems.- Random Phenomena in Nonlinear Systems in Connection with the Volterra Approach.- List of Contributors.