双稳态系统中随机共振和相干共振的相关性

摘要

研究了加性噪声和乘性噪声共同驱动的双稳态系统中的随机共振和相干共振现象。针对加性噪声和乘性噪声之间不存在关联性和存在关联性两种情形，引入一种适当的能同时表征随机共振和相干共振的指标，应用一阶欧拉方法，通过数值模拟对系统的随机共振和相干共振现象进行研究。结果表明在弱噪声驱动下，随着加性噪声强度的增加，当系统出现相干共振时，如果给系统外加一个弱周期驱动力，几乎在同一时刻，系统也出现了随机共振现象；但随着乘性噪声强度的增加，仅当加性噪声和乘性噪声之间相关时，此结论成立。并且系统参数对相干共振和随机共振的影响是一致的。%The phenomenon of stochastic resonance (SR) and coherence resonance (CR) in a bi-stable system driven by additive and mul-tiplicative noises has been investigated. For the case that the system has uncorrelated or correlated additive and multiplicative noises, we introduce an appropriate index that can characterize both SR and CR at the same time. Applying the first-order Euler numerical computation to study the SR and CR, We can show that for small noise density, with the increase of additive noise density, and the appearance of CR, if we add a small periodic force to the bi-stable system, SR will occur almost at the same time. However, with increasing multiplicative noise density, the above conclusion may be satisfied only for correlated additive and multiplicative noises. Moreover, the effects of other parameters on CR and SR can be shown to be the same.