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.
Inhaltsverzeichnis
Preface. 1. Mathematical Models of Deterministic Discrete and Distributed Dynamical Systems. 2. Order and Chaos as Two General Basic Trends in the Evolution of Dynamical Systems. 3. Stochasticity Transformers, Amplifiers and Generators. 4. Brief Survey of Studies Related to the Appearance of the Problem of Chaotic and Stochastic Motions and to Turbulence Theory. 5. Local Phase Portraits of the Simplest Steady-State Motions and their Bifurcations. 6. Stochastic and Chaotic Attractors. 7. Bifurcations and Routes to Chaos and Stochasticity. 8. Quantitative Characteristics of Stochastic and Chaotic Motions. Some Universal Properties in Order-Chaos and Transitions. 9. Examples of Mechanical, Physical, Chemical, and Biological Systems with Chaotic and Stochastic Motions. Bibliography. Index.
