The behavior of a periodically-forced nonlinear system subject to additive noise

Abstract

We continue the study of a nonlinear first-order dynamical system first considered by Chen. This model is characterized by a multiplicative periodic forcing term and additive dichotomous noise in place of the white noise of Chen's analysis. Two parameters are used to characterize the qualitative properties of such a system, the mean first-passage time to the ends of the interval and the Fourier spectrum generated by the solution of the equation. We show that the mean first-passage time is monotonic in the amplitude of the periodic force and exhibits a resonant dependence on its frequency. In addition the substitution of dichotomous for white noise leads to a systematic change in the ability to smooth out the peaks in the Fourier spectrum of the solution.