Stochastic and Chaotic Oscillations

✍ Scribed by Yu. I. Neimark, P. S. Landa (auth.)

Publisher: Springer Netherlands
Year: 1992
Tongue: English
Leaves: 509
Series: Mathematics and Its Applications Soviet Series 77
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This volume is devoted to stochastic and chaotic oscillations in dissipative systems.
Chapter 1 deals with mathematical models of deterministic, discrete and distributed dynamical systems. In Chapter 2, the two basic trends of order and chaos are considered. The next three chapters describe stochasticity transformers, amplifiers and generators, turbulence, and phase portraits of steady-state motions and their bifurcations. Chapter 6 treats the topics of stochastic and chaotic attractors, and this is followed by two chapters dealing with routes to chaos and the quantitative characteristics of stochastic and chaotic motions. Finally, Chapter 9, which comprises more than one-third of the book, presents examples of systems having chaotic and stochastic motions drawn from mechanical, physical, chemical and biological systems. The book concludes with a comprehensive bibliography.
For mathematicians, physicists, chemists and biologists interested in stochastic and chaotic oscillations in dynamical systems.

✦ Table of Contents

Front Matter....Pages i-xii
Mathematical Models of Deterministic Discrete and Continuous Dynamical Systems....Pages 1-39
Order and Chaos as Two General Basic Trends in the Evolution of Dynamical Systems....Pages 40-56
Stochasticity Transformers, Amplifiers and Generators....Pages 57-80
Brief Survey of Studies Related to the Appearance of the Problem of Chaotic and Stochastic Motions and to Turbulence Theory....Pages 81-96
Local Phase Portraits of the Simplest Steady-State Motions and Their Bifurcations....Pages 97-131
Stochastic and Chaotic Attractors....Pages 132-175
Bifurcations and Routes to Chaos and Stochasticity....Pages 177-240
Quantitative Characteristics of Stochastic and Chaotic Motions. Some Universal Properties in Order-Chaos and Inverse Transitions....Pages 241-291
Examples of Mechanical, Physical, Chemical, and Biological Systems with Chaotic and Stochastic Motions....Pages 293-441
Back Matter....Pages 443-500

✦ Subjects

Probability Theory and Stochastic Processes; Applications of Mathematics

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