Series Editor's Preface | |
Preface | |
Mathematical Models of Deterministic Discrete and Continuous Dynamical Systems | p. 1 |
Simplest typical models of discrete dynamical systems | p. 2 |
Chaotic motions of deterministic dynamical systems | p. 19 |
Simplest mathematical models of continuous dynamical systems | p. 25 |
Discrete version of continuous dynamical systems | p. 31 |
Models for locally active continuous media | p. 37 |
Order and Chaos as Two General Basic Trends in the Evolution of Dynamical Systems | p. 40 |
Order and chaos: stability and instability | p. 41 |
Time synchronization phenomena | p. 49 |
Spatial and temporal order and chaos | p. 52 |
Stochasticity Transformers, Amplifiers and Generators | p. 57 |
Stochasticity transformers | p. 57 |
Stochasticity amplifiers | p. 62 |
Stochasticity generators | p. 70 |
Is the stochasticity of stochastic and chaotic motions of deterministic dynamical systems real? | p. 78 |
Brief Survey of Studies Related to the Appearance of the Problem of Chaotic and Stochastic Motions and to Turbulence Theory | p. 81 |
Local Phase Portraits of the Simplest Steady-State Motions and Their Bifurcations | p. 97 |
Equilibrium states | p. 97 |
Bifurcations of equilibrium states | p. 103 |
Phase portraits in the vicinity of periodic motions | p. 115 |
Bifurcations of periodic motions | p. 116 |
Toroidal integral manifolds | p. 127 |
Stochastic and Chaotic Attractors | p. 132 |
Auxiliary mappings and sequences of point mappings | p. 134 |
Transition from the "negative" to the "positive" and investigation of typical appearance of chaos | p. 145 |
Conditions for the appearance of chaotic and stochastic attractors | p. 173 |
Bifurcations and Routes to Chaos and Stochasticity | p. 177 |
General description of the tree of possible bifurcations | p. 179 |
Series of bifurcations | p. 183 |
Bifurcations and the stochastic attractor in a Lorenz system | p. 201 |
Bifurcations and the phase portrait of parametrically excited oscillator or rotator | p. 215 |
On the appearance of chaos and stochasticity in dissipative dynamical systems | p. 231 |
Quantitative Characteristics of Stochastic and Chaotic Motions. Some Universal Properties in Order-Chaos and Inverse Transitions | p. 241 |
Statistical characteristics | p. 241 |
Lyapunov exponents. Dimension and entropy of a stochastic attractor | p. 252 |
Synchronization threshold as a quantitative characteristic of chaotic motions | p. 264 |
Certain universal laws in order-chaos transitions, and analogy with phase transitions | p. 266 |
"Examples of Mechanical, Physical, Chemical, and Biological Systems With Chaotic and Stochastic Motions | p. 293 |
Non-linear impact negative-friction oscillator and other systems with discontinuous characteristics | p. 293 |
Tunel-diode generators | p. 295 |
Non-linear oscillators with periodic external force | p. 298 |
Lorenz equations and other systems of order three | p. 322 |
Action of a harmonic external force on periodic and chaotic oscillation generators | p. 351 |
Interaction of oscillation generators of various kinds | p. 368 |
Certain discrete models of turbulence | p. 373 |
Examples of models for chemical kinetics | p. 383 |
Systems with delay and other continuous systems | p. 401 |
Stochasticity in quantum systems | p. 430 |
Bibliography | p. 443 |
Index | p. 499 |
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