| 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 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
