非线性动力系统分岔点邻域内随机共振的特性

研究了叉形分岔系统和FitzHugh Nagumo(FHN)细胞模型两种非线性动力系统分岔点邻域内 随机共振的特性.研究结果表明：这两种系统在分岔发生时具有由一个吸引子变为两个吸引 子或者由两个吸引子变为一个吸引子共同的分岔特性，即在分岔点的邻域内, 系统在分岔点 的两侧有分岔前吸引子和分岔后吸引子存在，在噪声的作用下，系统的运动除了像传统随机 共振的机理那样在分岔点一侧共存的吸引子之间跃迁，还在分岔点两侧三个吸引子（分岔前 一个吸引子和分岔后两个吸引子）之间跃迁，并且这种跃迁单独诱发了随机共振 ；在两种 跃迁都发生的情况下, 在其分岔点的邻域内，由第二种跃迁诱发的随机共振在引起第一种跃 迁噪声的强度很大的范围内变化仍可维持, 而第一种跃迁诱发的随机共振在引起第二种跃迁 噪声的强度很小的范围内变化即迅速消失. 关键词： 随机共振 吸引子 分岔点 跃迁

Characteristic of nonlinear system stochastic resonance in the neighbourhood of bifurcation point

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.