Foundations of synergetics II: chaos and noise
This book is the second of two volumes that together give a comprehensive introduction to the theory of cooperative behavior in active systems. This volume is devoted to the properties of the complex chaotic patterns that can arise in distributed active systems. The reader will encounter strange attractors, fractals, discrete maps, spatio-temporal chaos etc., and will learn how these phenomena relate to the emergence of complex and chaotic patterns. Examples are treated in detail. For this edition the chapter on turbulence in distributed active systems has been rewritten and one on the control of chaotic behaviour has been added. The second edition contains much new material and has been thoroughly revised.
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amplitude approximately asymptotic automata behavior bifurcation boundary breeding centers chaos chaotic dynamics Chap coefficient complex consider control parameter correlation function correlation radius corresponding defects dependence described determined deterministic diffusion dimensionality discrete domains dynamical system eigenvalues elements estimate evolution example explosion threshold exponentially fcbirth fcdeath finite fixed point fluctuations Fokker-Planck equation frequencies Gaussian Ginzburg-Landau equation given Hamiltonian systems Hence increase initial conditions integral intermittency internal noise interval iterative maps limit cycle linear logistic map Lorenz Lorenz model Lyapunov exponents medium nonlinear Note one-dimensional order parameter particles pattern periodic perturbation phase space phase trajectory phase transitions plane Poincare map population density probability distribution properties quasiperiodic motion random process reaction regime represents reproduction Sect sequence solution spatial species spectrum spikes spiral wave stable stationary statistical stochastic differential equation strange attractor torus total number transformation turbulence two-dimensional unstable variables variations vector velocity volume