Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- Introduction to Volume 1
- 1 Noise-activated escape from metastable states: an historical view
- 2 Some Markov methods in the theory of stochastic processes in nonlinear dynamical systems
- 3 Langevin equations with colored noise
- 4 First passage time problems for non-Markovian processes
- 5 The projection approach to the Fokker–Planck equation: applications to phenomenological stochastic equations with colored noises
- 6 Methods for solving Fokker–Planck equations with applications to bistable and periodic potentials
- 7 Macroscopic potentials, bifurcations and noise in dissipative systems
- 8 Transition phenomena in multidimensional systems – models of evolution
- 9 Colored noise in continuous dynamical systems: a functional calculus approach
- Appendix: On the statistical treatment of dynamical systems
- Index
Preface
Published online by Cambridge University Press: 05 January 2012
- Frontmatter
- Contents
- List of contributors
- Preface
- Introduction to Volume 1
- 1 Noise-activated escape from metastable states: an historical view
- 2 Some Markov methods in the theory of stochastic processes in nonlinear dynamical systems
- 3 Langevin equations with colored noise
- 4 First passage time problems for non-Markovian processes
- 5 The projection approach to the Fokker–Planck equation: applications to phenomenological stochastic equations with colored noises
- 6 Methods for solving Fokker–Planck equations with applications to bistable and periodic potentials
- 7 Macroscopic potentials, bifurcations and noise in dissipative systems
- 8 Transition phenomena in multidimensional systems – models of evolution
- 9 Colored noise in continuous dynamical systems: a functional calculus approach
- Appendix: On the statistical treatment of dynamical systems
- Index
Summary
All macroscopic physical systems are subject to fluctuations or noise. One of the most useful and interesting developments in modern statistical mechanics has been the realization that even complex non-equilibrium systems can often be reduced to equivalent ones of only a few degrees of freedom by the elimination of dynamically non-relevant variables. Theoretical descriptions of such contracted systems necessarily begin with a set of either continuous or discrete dynamical equations, which can then be used to describe noise driven systems with the inclusion of random terms. Studies of these stochastic dynamical equations have expanded rapidly in the past two decades, so that today an exuberant theoretical activity, a few experiments, and a remarkably large number of applications, some with challenging technological implications, are evident.
The purpose of these volumes is twofold. First we hope that their publication will help to stimulate new experimental activity by contrasting the smallness of the number of existing experiments with the many research opportunities raised by the chapters on applications. Secondly, it has been our aim to collect together in one place a complete set of authoritative reviews with contributions representative of all the major practitioners in the field. We recognize that as an inevitable consequence of the intended comprehensiveness, there will be few readers who will wish to digest these volumes in their entirety. We trust, instead, that readers will be stimulated to choose from the many possibilities for new research represented herein, and that they will find all the specialised tools, be they experimental or theoretical, that they are likely to require.
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- Information
- Noise in Nonlinear Dynamical Systems , pp. xiii - xivPublisher: Cambridge University PressPrint publication year: 1989