Springer Synergetics

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.