双稳系统随机共振效应的数值分析

Numerical Research on Stochastic Resonance Effect in Bistable System

以绝热近似随机共振理论为基础,分析了双稳系统随机共振模型,研究系统参数、噪声强度、信号幅值和频率变化对双稳系统随机共振效应的影响。通过分析得出,输入信号和系统参数一定时,系统发生随机共振所需要的噪声存在一个最佳强度;信号幅值的增大有利于随机共振效应的产生;信号频率的增大将使输出功率谱信号频率处谱峰逐渐离开噪声能量集中的低频区,且谱峰幅度逐渐减小,随机共振效应逐渐弱化消失。针对信号幅值、频率、噪声强度超出绝热近似理论的小参数要求而成为大参数,对变尺度方法实现大参数信号的随机共振进行分析和评述。

The model of stochastic resonance in bistable system is analyzed based on adiabatic approximate theory.Ingredients of stochastic resonance,including system parameters,noise intensity,signal amplitude and frequency,are studied.It is concluded that there is an optimal noise intensity for the stochastic resonance system,and augmentation of the signal amplitude is favorable to the occurrence of stochastic resonance.However,the increase of signal frequency will cause the peak of signal in output power spectrum to leave the low-frequency area that noise energy concentrates on.It makes the peak of signal decrease rapidly and the stochastic resonance phenomena disappear gradually.For the fact that signal amplitude,frequency,noise intensity often exceed the requirements of small parameters in the adiabatic approximation theory and turn into large parameters,the re-scaling method for realization of stochastic resonance of large parameter signals is discussed.