Behavior of Bistable Oscillatory System with Random External Force

Abstract

In this paper an oscillatory system which has two stable oscillatory modes and is disturbed by random external force is considered. In the deterministic case, the state settles to a stable point which is determined by the initial condition. If the random input is applied to this system, an interesting statistical phenomenon is seen that the state moves between both modes. For the oscillatory systems the averaging method is useful. The stochastic differential equations in regard to the amplitude and phase are obtained and the system is analyzed on the basis of them. First the behaviour of the steady state is considered. Secondly the first passage time problem, namely the time which the state takes to make transition to another stable area leaving one stable area, is discussed. The analytic results are compared with those obtained by the digital simulation.