The Maximal Lyapunov Exponent of a Stochastic Bautin Bifurcation System

Abstract

In this paper, we investigate the maximal Lyapunov exponent of a Bautin bifurcation system with additive white noise, which is also the fifth-order truncated normal form of a generalized Hopf bifurcation in the absence of noise. By solving the stationary density associated with the invariant measure of the system and its marginal distribution, we show that the maximal Lyapunov exponent is of indefinite sign depending on parameters and we give the explicit condition to control the range of the maximal Lyapunov exponent. Finally, we give the asymptotic expansion of the maximal Lyapunov exponent in the small noise limit.