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Foundations of Synergetics II : Complex Patterns

Author: Alexander S Mikhailov; A Yu Loskutov
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1991.
Series: Springer series in synergetics, 52.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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 ..., and will learn how these phenomena relate to the emergence  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Alexander S Mikhailov; A Yu Loskutov
ISBN: 9783642972942 3642972942
OCLC Number: 851393332
Description: 1 online resource (viii, 210 pages 98 illustrations).
Contents: 1. Introduction --
1.1 Chaotic Dynamics --
1.2 Noise-Induced Complex Patterns --
1.3 Chaos and Self-Organization --
2. Unpredictable Dynamics --
2.1 Hamiltonian Systems --
2.2 Destruction of Tori --
2.3 Ergodicity and Mixing --
3. Strange Attractors --
3.1 Dissipative Systems and Their Attractors --
3.2 The Lorenz Model --
3.3 Lyapunov Exponents --
3.4 The Autocorrelation Function --
4. Fractals --
4.1 Self-Similar Patterns --
4.2 Dimensions --
4.3 Fractal Dimensions of Strange Attractors --
5. Discrete Maps --
5.1 Fixed Points and Cycles --
5.2 Chaotic Maps --
5.3 Feigenbaum Universality --
6. Routes to Temporal Chaos --
6.1 Bifurcations --
6.2 The Ruelle-Takens Scenario --
6.3 Period Doubling --
6.4 Intermittency --
7. Spatio-Temporal Chaos --
7.1 Embedding Dimensions --
7.2 Phase Turbulence --
7.3 Coupled Chaotic Maps --
8. Random Processes --
8.1 Probabilistic Automata --
8.2 Continuous Random Processes --
8.3 The Fokker-Planck Equation --
9. Active Systems with Noise --
9.1 Generalized Brownian Motion --
9.2 Internal Noise --
9.3 Optimal Fluctuations --
10. Population Explosions --
10.1 Mean Ignition Time of Explosion --
10.2 Intermittency of Growth --
10.3 Breeding Centers --
11. Extinction and Long-Time Relaxation --
11.1 Random Traps --
11.2 Irreversible Annihilation --
11.3 Conserved Quantities and Long-Time Relaxation --
11.4 Stochastic Segregation and the Sub-Poissonian Distribution --
12. Catastrophes --
12.1 Second-Order Phase Transitions --
12.2 Sweeping Through the Critical Region --
12.3 The Biased Transition --
12.4 Population Settling-Down --
12.5 Survival in the Fluctuating Environment --
References.
Series Title: Springer series in synergetics, 52.
Responsibility: by Alexander S. Mikhailov, Alexander Yu. Loskutov.
More information:

Abstract:

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 ..., and will learn how these phenomena relate to the emergence of complex and chaotic patterns. Examples treated in detail include population explosion and extinction in fluctuating distributed media, and fluctuation effects in binary annihilation.

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