Alexander S. Mikhailov, Alexander Yu. Loskutov

Foundations of Synergetics II (eBook, PDF)

Chaos and Noise

• Format: PDF

Produktbeschreibung

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 treated in detail include population explosion and extinction in fluctuating distributed media, and fluctuation effects in binary annihilation. This second edition has been revised and enlarged, in particular with respect to turbulence in distributed active systems, and a new section on control of chaotic behavior has been added. Much new material has been included in chapters where noise-induced pattern formation is considered.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 278
• Erscheinungstermin: 8. März 2013
• Englisch
• ISBN-13: 9783642801969
• Artikelnr.: 53173976

Autorenporträt

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 partner volume I 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 undergraduates. The second edition is essentially revised and enlarged.

Inhaltsangabe

1. Introduction.- 1.1 Chaotic Dynamics.- 1.2 Noise-Induced Complex Patterns.- 1.3 Chaos, Noise, 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 Fractal Dimensions.- 4.3 Dimensions of Strange Attractors and Fractal Basin Boundaries.- 5. Iterative 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.- 6.5 Controlling Chaotic Behavior.- 7. Spatiotemporal Chaos.- 7.1 Analysis of Time Series.- 7.2 Turbulence in Distributed Active Systems.- 7.3 Coupled Chaotic Maps.- 7.4 The Complex Ginzburg-Landau Equation.- 7.5 Statistics of Defects.- 7.6 Transient Turbulence.- 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 and Transition Probabilities.- 10. Birth-Death Systems.- 10.1 Stochastic Birth-Death Models.- 10.2 The Ignition Problem.- 10.3 Spatiotemporal Intermittency in Population Explosions.- 10.4 Explosions in Media with Random Breeding Centers.- 11. Extinction and Complex Relaxation.- 11.1 Diffusion with Random Traps.- 11.2 Irreversible Annihilation.- 11.3 Conserved Quantities and Long-Time Relaxation.- 11.4 Stochastic Segregation.- 12. Nonequilibrium Phase Transitions.- 12.1 Second-Order Phase Transitions.- 12.2 Sweeping Through the Critical Region.- 12.3 The Biased Transition.- 12.4 Medium-Populating Transitions.- 12.5 Noise-Induced Phase Transitions: Competition and Coexistence in the Fluctuating Environment.- References.