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Dynamical Systems Perturbed by Noise: the Langevin Equation

  • Johan Grasman
  • Onno A. van Herwaarden
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

In this monograph we analyse the dynamics of finite-dimensional nonlinear systems that are perturbed by noise. The type of systems we deal with arises in different fields of applications, such as in stochastic mechanics and in the dynamics of biological populations. Depending on the application, the noise may have quite different origins. Outside fluctuations affecting a physical system can be incorporated in the modelling in the form of a stochastic input. The system may have intrinsic stochastics, for example in the birth-death process in population dynamics. Another possibility is to account for components neglected in the model by adding noise terms. As a result of the noise the value of the state vector X(t) of a system is uncertain.

Keywords

Wiener Process Langevin Equation Stochastic Input Forward Euler Scheme Autonomous Nonlinear System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Johan Grasman
    • 1
  • Onno A. van Herwaarden
    • 1
  1. 1.Department of MathematicsAgricultural UniversityWageningenThe Netherlands

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