Stochastic bifurcation for two-time-scale dynamical system with <i>α</i> -stable Lévy noise

Abstract

Abstract This work focuses on stochastic bifurcation for a slow–fast dynamical system driven by non-Gaussian α -stable Lévy noise. We prove the main result for the stochastic equilibrium states for the original system and the reduced system based on the random slow manifold. Then, it is verified that the slow reduced system bears the stochastic bifurcation phenomenon inherited from the original system. Furthermore, we investigate the number and stability type of stochastic equilibrium states for dynamical systems through numerical simulations, and it is illustrated that the slow reduced system captures the stochastic bifurcation of the original system.