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Foundations of Synergetics II - Alexander S. Mikhailov, Alexander Yu. Loskutov

Foundations of Synergetics II

Complex Patterns
Buch | Softcover
VIII, 210 Seiten
2012 | 1. Softcover reprint of the original 1st ed. 1991
Springer Berlin (Verlag)
978-3-642-97296-6 (ISBN)
CHF 74,85 inkl. MwSt
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.

The subject of chaos and, in particular, the complex chaotic patterns that can arise in distributed active systems are topics that are currently attracting much attention from various branches of science. This book and its recently published partner volume offer an excellent introduction to the basic theory of cooperative behavior in distributed active systems and are written at a level that is accessible to undergraduate students.

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.

Erscheint lt. Verlag 19.1.2012
Reihe/Serie Springer Series in Synergetics
Zusatzinfo VIII, 210 p.
Verlagsort Berlin
Sprache englisch
Maße 170 x 242 mm
Gewicht 391 g
Themenwelt Naturwissenschaften Physik / Astronomie Allgemeines / Lexika
Naturwissenschaften Physik / Astronomie Theoretische Physik
Schlagworte Chaos • Noise • Pattern • random processes • reaction-diffusion systems • Reaction-Diiffusion Systems • Synergetik • Turbulence • Verteilte Verarbeitung
ISBN-10 3-642-97296-9 / 3642972969
ISBN-13 978-3-642-97296-6 / 9783642972966
Zustand Neuware
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