非对称双稳耦合网络系统的尺度随机共振研究

研究了不同周期信号调制下非对称双稳耦合网络系统的尺度随机共振问题. 针对该网络系统, 首先运用高斯近似和役使原理对其进行了降维, 推导了其简化模型. 在绝热近似条件下, 利用Fokker-Planck方程分别得到了余弦信号和矩形信号调制下信噪比的解析表达式. 在此基础上, 研究了系统的尺度随机共振行为, 并讨论了非对称性、噪声强度、周期信号的振幅和耦合系数对系统尺度随机共振的影响. 结果表明, 两种情形下信噪比均是系统尺度的非单调函数, 说明在此网络系统中产生了共振现象.关键词：尺度随机共振非对称双稳耦合网络系统余弦信号矩形信号

System size sto chastic resonance in asymmetric bistable coupled network systems

In this paper, the noise-induced dynamics is studied in an asymmetric bistable coupled network system modulated by different signals. According to the Gaussian approximation and the slaving principle, the asymmetric bistable coupled network system is reduced to a low-dimensional model with two potentials, by which the phenomenon of system size stochastic resonance is studied theoretically and numerically. Under the assumption of adiabatic limit, the expressions of signal-to-noise ratio (SNR) are found by virtue of Fokker-Planck equation with respect to cosine signal and rectangle signal, based on which the system size stochastic resonance is investigated. Further, the effects of the noise strength, the asymmetry and the amplitude of the signal on the system size stochastic resonance are well discussed. It is demonstrated that the SNR shows a non-monotonic dependence on the number of coupled systems, which is demonstrated that there is a resonance with respect to the number of coupled systems.
Keywords：system size stochastic resonanceasymmetric bistable coupled network systemscosine signalrectangle signal