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Stochastic Model

  • Peter A. Tass
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

The goal of this chapter is to present a model equation which describes the behavior of a population of interacting phase oscillators subjected to stimulation and random forces. With this aim in view first a stochastic differential equation, a so-called Langevin equation will be derived which describes how the oscillators’ phase dynamics is influenced by their mutual interactions, by the stimulus and by the random forces. As a consequence of the presence of noise the cluster of oscillators does not move along a trajectory as it is known from systems without noise. Rather the system is permanently kicked by the random forces while its dynamics evolves in time. Hence, we have to deal with a stochastic description of the phase dynamics.

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Literatur

  1. Best, E.N. (1979): Null space in the Hodgkin-Huxley equations: a critical test, Biophys. J. 27, 87–104Google Scholar
  2. Gardiner, C.W. (1985): Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd. ed., Springer, BerlinGoogle Scholar
  3. Haken, H. (1977): Synergetics, An Introduction, Springer, Berlin; (1983): Advanced Synergetics, Springer, BerlinGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Peter A. Tass
    • 1
  1. 1.Neurologische KlinikHeinrich-Heine-UniversitätDüsseldorfGermany

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