Logo - springer
Slogan - springer

Computer Science - Image Processing | Foundations of Synergetics II - Chaos and Noise

Foundations of Synergetics II

Chaos and Noise

Mikhailov, Alexander, Loskutov, Alexander Yu.

2nd ed. 1996. Softcover reprint of the original 2nd ed. 1996, X, 277 pp. 120 figs.

Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-3-642-80196-9

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase

learn more about Springer eBooks

add to marked items


Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-3-642-80198-3

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

  • About this book

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.

Content Level » Research

Keywords » Reaction-Diffusion Systems - Reaction-Diiffusion Systems - Synergetik - Turbulence - Verteilte Verarbeitung - chaos - noise - pattern - random processes

Related subjects » Classical Continuum Physics - Complexity - Economic Theory - Image Processing - Life Sciences, Medicine & Health - Theoretical and Computational Chemistry

Table of contents 

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.

Popular Content within this publication 



Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Pattern Recognition.