UID:
almahu_9949199406002882
Format:
VIII, 210 p.
,
online resource.
Edition:
1st ed. 1991.
ISBN:
9783642972942
Series Statement:
Springer Series in Synergetics, 52
Content:
This textbook is based on a lecture course in synergetics given at the University of Moscow. In this second of two volumes, we discuss the emergence and properties of complex chaotic patterns in distributed active systems. Such patterns can be produced autonomously by a system, or can result from selective amplification of fluctuations caused by external weak noise. Although the material in this book is often described by refined mathematical theories, we have tried to avoid a formal mathematical style. Instead of rigorous proofs, the reader will usually be offered only "demonstrations" (the term used by Prof. V. I. Arnold) to encourage intuitive understanding of a problem and to explain why a particular statement seems plausible. We also refrained from detailing concrete applications in physics or in other scientific fields, so that the book can be used by students of different disciplines. While preparing the lecture course and producing this book, we had intensive discussions with and asked the advice of Prof. V. I. Arnold, Prof. S. Grossmann, Prof. H. Haken, Prof. Yu. L. Klimontovich, Prof. R. L. Stratonovich and Prof. Ya.
Note:
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.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783642972966
Additional Edition:
Printed edition: ISBN 9783540534488
Additional Edition:
Printed edition: ISBN 9783642972959
Language:
English
DOI:
10.1007/978-3-642-97294-2
URL:
https://doi.org/10.1007/978-3-642-97294-2
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