四稳系统的双重随机共振特性

Double stochastic resonance characteristics of quad-stable system

提出了一类8次势函数并讨论了其分岔特性,得到由左、右2个小尺度双稳势和中间势垒构成的对称四稳系统.建立了在周期力和随机力共同作用下四稳系统输出响应的近似解析表达式,并从能量角度引入功这一过程量来刻画大、小不同尺度双稳势之间的作功能力,发现四稳势中存在着双重随机共振现象.理论分析与数值仿真结果表明,当中间势垒高度大于左右2个小尺度双稳势的势垒高度时,四稳系统的响应随着噪声强度的变化由束缚在小尺度双稳系统中做小幅振动转变为跨越中间势垒的大幅振动,功随噪声强度的变化出现了双峰曲线,存在着双重随机共振,且小尺度随机共振能增强大尺度随机共振的效应.

In this paper we propose a class of 8th-order potential function,and discuss the bifurcation characteristic of such a system in detail.Then,a symmetric quad-stable system consisting of two small-scale bistable potentials on the left and right and an intermediate barrier is obtained.In order to analyze the quad-stable system characteristic effectively,under the combined action of periodic force and random force,the approximate analytical expression of the quad-stable system output response is established.Meanwhile,from the viewpoint of the energy,the work which is a process quantity is introduced to describe the capacity for work between the large-scale and small-scale bistable potential.It is found that the double stochastic resonance phenomenon does exist in the quad-stable system.The theoretical analysis and numerical simulation results indicate that when the height of the intermediate barrier is higher than the barrier height of the two small-scale bistable potentials on the left and right,as the noise intensity increases,the response of the quad-stable system transforms a smallamplitude vibration restricted in a small-scale bistable subsystem into a large-amplitude vibration across the intermediate barrier,and the work done by the periodic force presents a double-peak curve.To be more specific,as the noise intensity gradually increases from zero,the system response is first confined to a small-scale bistable potential.Under the joint action of the small-scale bistable potential,periodic force and random force,the small-scale stochastic resonance phenomenon occurs,and the first resonance peak appears.With the noise intensity increasing even further,the system response turns into the large-amplitude vibration between two small-scale bistable subsystems,resulting in the large-scale stochastic resonance phenomenon and a higher resonance peak.Thus,the work done by periodic force has the peak values at two different noise intensities,which means that the noise can induce the double stochastic resonance phenomenon in the quad-stable system.More importantly,it can be found that the small-scale stochastic resonance can enhance the effect of large-scale stochastic resonance.