by T Kapitaniak (Tech. Univ. of Lodz, Poland)

As in the first edition, the influence of random noise on the chaotic behavior of dissipative dynamical systems is investigated. Problems are illustrated by mechanical examples. This revised and updated edition contains new sections on the summary of probability theory, homoclinic chaos, Melnikov method, routes to chaos, stabilization of period-doubling, and Hopf bifurcation by noise. Some chapters have been rewritten and new examples have been added.

• Probability Theory — Brief Summary
• Chaotic and Stochastic Processes
• Noisy Dynamical Systems
• Fokker — Planck — Kolmogorov Equation
• Multi-Maxima Probability Density Functions
• Random Lyapunov Exponents
• Poincare Maps for Noisy Systems
• Regular and Chaotic Stochastic Processes
• Stochastic Sensitivity Functions and Chaos
• Homoclinic Chaos Perturbated by Noise
• Examples
• Noisy Routes to Chaos
• References