STOCHASTIC PHASE LOCKINGS IN A RELAXATION-OSCILLATOR FORCED BY A PERIODIC INPUT WITH ADDITIVE NOISE - A FIRST-PASSAGE-TIME APPROACH

Noise effects on phase lockings in a system consisting of a piecewise- linear van der Pol relaxation oscillator driven by a periodic input ar e studied. The problem of finding the period of the oscillator is redu ced to the first-passage-time problem of the Ornstein-Uhlenbeck proces s with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a tr ansition 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.