Stochastic resonance of a pitchfork bifurcation system

In previous studies of stochastic resonance for a pitchfork bifurcation system, it is usually considered that the system motion transits between two stable fixed points under the perturbation of an external noise. The present paper has focused on the different cases in which the system state is considered to be in the small neighborhood of bifurcation point under three different types of perturbations: an internal noise only, or an external noise only, or combination of an internal noise and an external noise. Monte Carlo simulations are carried out for the investigation, and the numerical results reveal the characteristics of stochastic resonance in these cases.