THE CORRESPONDENCE BETWEEN STOCHASTIC RESONANCE AND BIFURCATION OF MOMENT EQUATIONS OF NOISY NONLINEAR DYNAMICAL SYSTEM

Abstract

There is a kind of correspondence between stochastic resonance and bifurcation of the moment equations of a noisy nonlinear system with the same noise intensity as the resonance independent variable and the bifurcation parameter, respectively. In this paper, this correspondence is examined and revealed in the noisy one-dimensional bistable system and the noisy two-dimensional Duffing oscillator. The bifurcation of the moment equations of each noisy system is the bifurcation with double-branch of fixed-point shift. Besides classical stochastic resonance, a kind of complex stochastic resonance corresponds to the bifurcation of moment equations. This complex stochastic resonance is induced by the stochastic transitions of system motion among the three fixed point attractors on both sides of the bifurcation point of the original system, which is predicted semi-analytically. Finally, due to this correspondence being examined, the mechanism of stochastic resonance can be provided through analyzing the change of the energy transfer induced by the bifurcation of the moment equations.