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From instability to intelligence: complexity and predictability in nonlinear dynamics. (English) Zbl 0926.37012

Lecture Notes in Physics. New Series m: Monographs. m49. Berlin: Springer. xiv, 552 p. (1997).
This book is about “good” instabilities, which lead to change evolution, progress, creativity and intelligence. The main emphasis is on intrinsic stochasticity caused by the instability of dynamical systems.
In particular, the authors present for the first time in book form their concept of terminal (non Lipschitz) dynamics. They explain that instability as an attribute of dynamical models can explain the paradox of irreversibility in thermodynamics, the phenomenon of chaos and turbulence in classical mechanics, and multi-choice behavior in biological and social systems.
The monograph treats impredictibility in nonlinear dynamics and its applications to information processing. For studying this intrinsic stochasticity caused by the instability of governing dynamical equations, one uses a new approach based upon a revision of the mathematical formalism of Newtonian dynamics, and, in particular, upon elimination of requirements concerning differentiability, which in some cases lead to unrealistic solutions. This new mathematical formalism allows to re-evaluate the view on the origin of chaos and turbulence, on prediction of their probabilistic structures, and on their role in information processing in biological systems. This is the first part of the book. The second part describes these instabilities and their usefulness in physics, biology, neural nets, creativity, intelligence and social behavior.
The monograph is intended to be a self-contained text for physicists, biologists, and engineers who wish to apply methods of nonlinear dynamics to the problems of artificial intelligence, neural networks, and information processing in general. It may also be useful to scientists who are interested in the theory of chaos and turbulence, and their applications in physics, biology and social sciences. It should also be of interest to philosophers of science.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N25 Dynamical systems in biology
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
92B20 Neural networks for/in biological studies, artificial life and related topics
82C32 Neural nets applied to problems in time-dependent statistical mechanics
76F20 Dynamical systems approach to turbulence
91C99 Social and behavioral sciences: general topics
00A69 General applied mathematics
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