(1) Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University, 560 Toyonaka, Osaka, Japan;(2) Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, 80126 Naples, Italy
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.