(1) Department of Electrical Engineering, Faculty of Engineering, Osaka University, Suita, 565, Japan;(2) Department of Computer and Business, Koka Women's College, Nishikyogoku, Kyoto, 615, Japan
Abstract:
Noise effects on the phase lockings and bifurcations in the sinusoidally forced van der Pol relaxation oscillator are investigated. Deterministic (noise-free) one-dimensional Poincaré mapping is extended to the iteration of the operator defined by a stochastic kernel function. Stochastic phase lockings and bifurcations are analyzed in terms of the density evolution by the operator. In particular, a new method which uses spectra (eigenvalues and eigenfunctions) of the operator to analyze stochastic bifurcations intensively is proposed.