Escape through an unstable limit cycle: Resonant activation

Abstract

We consider a Brownian particle acted on by a linear conservative force, a nonlinear frictional force, and multiplicative colored and additive white noises; the frictional force can be negative when the external energy supply is large enough. We numerically calculate the mean first passage time (MFPT) for the particle to escape from an unstable limit cycle and find resonant activation, i.e., the MFPT first decreases, followed by a rise after passing through a minimum with increasing noise correlation time tau for a fixed noise variance. For fixed noise strength of the multiplicative noise the MFPT increases linearly with tau. This is in sharp contrast to the case of fluctuations of nonlinear potentials, in which the MFPT first increases nonlinearly before reaching a limiting value. Our model could be useful for understanding some biological processes.