Characteristic of nonlinear system stochastic resonance in the neighbourhood of bifurcation point
非线性动力系统分岔点邻域内随机共振的特性

This paper studied the characteristics of stochastic resonance in the neighborho od of bifurcation point of two nonlinear dynamic systems, the pitchfork bifurcat ion system and FitzHugh-Nagumo (FHN) cell model. The results of research show that the two nonlinear dynamic systems have the same bifurcation characteristic of transition from one to two attractors (or from two to one attractors) when the bifurcation of each system occurs, that is, in the neighborhood of the bifurcation point there exist attractors before and after bifurcation on t he both sides of the bifurcation point. Under the perturbation of noise, a trans ition may occur between the two coexisting attractors on the right side of the b ifurcation point, in a way like the mechanism of traditional stochastic resonanc e; moreover,another transition may also occur among the three attractors (one be fore bifurcation and two after it) on two sides of the bifurcation point, which can induce stochastic resonance alone. When the two types of transitions occur, the stochastic resonance induced by the second type of transition continues in a wide intensity range of noise, which causes the first ty pe of transition; and the stochastic resonance induced by the first type of tran sition stops in a rather small range of the noise intensity,and then causes the second type of transition.