A study on stochastic resonance of one-dimensional bistable system in the neighborhood of bifurcation point with the moment method (Q813487)

The authors consider a bistable dynamical system described by the following Stratonovich equation: \[ dx(t)=[\mu x(t)-x(t)^3+A\sin(\omega t)]\,dt+\sqrt{2D_i}x(t)\circ dW_1 (t)+\sqrt{2D_e}\, dW_2(t), \] where \(W_1\) and \(W_2\) are two independent standard Brownian motions. The spectral power amplification factor is studied numerically in the neighbourhood of the bifurcation point \(\mu=0\) for different values of noise intensities \(D_i\) and \(D_e\). A bifurcation behaviour of moment equations is discussed.