Abstract
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.
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Tateno, T., Doi, S., Sato, S. et al. Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach. J Stat Phys 78, 917–935 (1995). https://doi.org/10.1007/BF02183694
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DOI: https://doi.org/10.1007/BF02183694