Stochastic Dynamics, born almost 100 years ago with the early explanations of Brownian motion by physicists, is nowadays a quickly expanding field of research within nonequilibrium statistical physics. The present volume provides a survey on the influence of fluctuations in nonlinear dynamics. It addresses specialists, although the intention of this book is to provide teachers and students with a reliable resource for seminar work. In particular, the reader will find many examples illustrating the theory as well as a host of recent findings.
Probability in physics.- From stratonovich calculus to noise-induced phase transitions.- Generalized langevin equations: A useful tool for the perplexed modeller of nonequilibrium fluctuations?.- Colored noise in dynamical systems: Some exact solutions.- On the operator method of variable contraction for stochastic processes.- Recurrence time statistics in low-dimensional dynamical systems.- The boltzmann equation for the gas of partly inelastic balls with regard to random interaction forces.- Ratchets driven by colored gaussian noise.- A motor protein model and how it relates to stochastic resonance, feynman's ratchet, and maxwell's demon.- A diffusion-limited reaction.- Stochastic localization in soft anharmonic oscillators.- Quantum transition state theory for multidimensional dissipative systems.- Surmounting fluctuating barriers: Basic concepts and results.- Some problems of cluster dynamics of biological macromolecules.- Stochastic synchronization.- Stochastic analysis of limit cycle behavior.- Symbolic dynamics approach to stochastic processes.- Stochastic resonance (for beginners).- Dynamics of globally coupled noisy oscillators.- Cluster statistics and traffic on a lattice.- Phase synchronization in noisy and chaotic oscillators.- A glauber-dynamics approach to coupled stochastic resonators.- Stochastic aspects of the force network in a regular granular piling.- Burgers' turbulence and dynamical scaling.- Quantum mechanics simulated by diffusion and branching processes.- Markov chain models for spatially-distributed reacting systems.- Macromechanical modeling of the surface flow of granular systems.- Novel pattern formation in granular matter.- Self-motion in physico-chemical systems far from thermal equilibrium.- Synthetic random flows: Generation and applications.- Active brownian particles: Artificial agents in physics.- Planetary rings nonequilibrium systems in space.