Stochastic Processes in Self-Excited Oscillation

Abstract

The amplitude and phase fluctuations in self-excited oscillation are studied phenomenologically using a van der Pol type stochastic equation. The second-order differential equation is converted into two first-order differential equations for the amplitude and the phase and their probability distributions are derived from the associated Fokker-Planck equations. The probability distribution of the amplitude around its most probable value is anomalously broadened and non-Gaussian near threshold of oscillation. The fluctuation in the oscillatory state is rather quasi-Gaussian. The growth of the time coherence of phase above threshold is accounted for to be due to a decrease in an apparent diffusion coefficient for phase fluctuation