Applied Chaos Theory: A Paradigm for ComplexityThis book differs from others on Chaos Theory in that it focuses on its applications for understanding complex phenomena. The emphasis is on the interpretation of the equations rather than on the details of the mathematical derivations. The presentation is interdisciplinary in its approach to real-life problems: it integrates nonlinear dynamics, nonequilibrium thermodynamics, information theory, and fractal geometry. An effort has been made to present the material ina reader-friendly manner, and examples are chosen from real life situations. Recent findings on the diagnostics and control of chaos are presented, and suggestions are made for setting up a simple laboratory. Included is a list of topics for further discussion that may serve not only for personal practice or homework, but also as themes for theses, dissertations, and research proposals.
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Contents
The Diagnostics and Control of Chaos | 11 |
The Anatomy of Systems and Structures | 41 |
Attractors | 59 |
Copyright | |
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algorithm applications behavior bifurcation Boltzmann cells chaos theory chaotic attractors chapter Clausius complex systems concept considered denotes depends deterministic differential discrete logistic equation discuss dissipative systems Duffing equation dynamical systems energy equilibrium ergodicity example exponential Fibonacci Figure fixed-point attractor flow follows fractal dimensions function growth hence increase initial conditions irreversible isolated systems Kolmogorov entropy limit cycle linear logistic curve logistic equation Lyapunov dimension Lyapunov exponent macroscopic Mandelbrot mathematical measure mechanics molecules namely nonequilibrium Nonlinear Dynamics occur open systems oscillator oscillatory parameter particles pendulum phase space phenomena physics Poincaré population position predator-prey Prigogine problems random reactions Reynolds number scale Schaffer self-organizing Shannon shown in Fig Sierpinsky triangle stable statistical entropy strange attractors structure technologies temperature term thermodynamics trajectories uncertainty Univ University unstable variable velocity volume W. H. Freeman Wiley & Sons xn+1 York