Journal of Statistical Physics

, Volume 78, Issue 3–4, pp 917–935 | Cite as

Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

  • Takashi Tateno
  • Shinji Doi
  • Shunsuke Sato
  • Luigi M. Ricciardi


Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.

Key Words

Additive noise relaxation oscillation van der Pol oscillator first-passage time stochastic phase locking Ornstein-Uhlenbeck process 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Takashi Tateno
    • 1
  • Shinji Doi
    • 1
  • Shunsuke Sato
    • 1
  • Luigi M. Ricciardi
    • 1
    • 2
  1. 1.Department of Biophysical Engineering, Faculty of Engineering ScienceOsaka UniversityToyonaka, OsakaJapan
  2. 2.Dipartimento di Matematica e ApplicazioniUniversità di Napoli “Federico II”NaplesItaly

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