Logical stochastic resonance in triple-well potential systems driven by colored noise.
Logical stochastic resonance in triple-well potential systems driven by colored noise.
复制标题
DOI：
10.1063/1.4768729
复制
发表时间：
2012-11
期刊：
影响因子：
2.9
通讯作者：
Huiqing Zhang;Yong Xu;Wei Xu;Xiuchun Li
中科院分区：
文献类型：
--
作者：
Huiqing Zhang;Yong Xu;Wei Xu;Xiuchun Li
在这项工作中，研究了一类随机三阱势系统中的逻辑随机共振（LSR）现象。首先利用解耦近似得到近似的Fokker-Planck方程。然后，我们证明在某些情况下，LSR 可以通过加性或乘性高斯有色噪声成功诱导。在没有内部噪声的情况下，对于 a = 0（参数 a 表征势阱的深度），LSR 实现似乎是不可能的，因为两侧的势阱太深，以至于当输入信号为 0 时，粒子无法跳过势垒进入中间势阱。随着 a 的增加，出现产生灵活逻辑门的最佳噪声带，并随着噪声相关时间的增加而移动到更高的噪声水平。与高斯白噪声相比，随着噪声颜色的增加，潜在深度参数a和加性噪声强度D在参数平面上的可靠区域先扩大后缩小。此外，还研究了乘性高斯有色噪声对 LSR 的影响。研究发现，由于乘性高斯有色噪声强烈影响势函数的形状，因此当 a = 0 时可以产生灵活可靠的逻辑行为。随着 a 的增加，即 a = 0.25，乘法高斯白噪声无法产生所需的逻辑行为。幸运的是，通过调整高斯有色噪声的相关时间也可以预期LSR。还可以观察到，对于高斯白噪声的情况，潜在深度参数a和乘性噪声强度Q的参数平面中的可靠区域较小，并且随着噪声颜色的增加而变大。
In this work, the logic stochastic resonance (LSR) phenomenon in a class of stochastic triple-well potential systems is investigated. Approximate Fokker-Planck equation is first obtained by using decoupling approximation. Then, we show that LSR can be successfully induced by additive or multiplicative Gaussian colored noise in some cases. In the absence of internal noise, LSR implementation seems impossible for a = 0 (The parameter a characterizes the depth of the potential well) since the two side wells are so deep that the particle cannot hop over the barrier into the middle well when the input signal is 0. With the increasing of a, the optimal noise band to yield flexible logic gates appears and moves to higher level of noise as the correlation time of noise increases. Compared with the Gaussian white noise, the reliable region in the parameter plane of potential depth parameter a and additive noise strength D first expands and then shrinks with increasing noise color. Furthermore, the effects of multiplicative Gaussian colored noise on LSR are investigated. It was found that the flexible and reliable logic behavior can be yielded for a = 0 due to the fact that the multiplicative Gaussian colored noise strongly affects the shape of the potential function. With the increasing of a, i.e., a = 0.25, multiplicative Gaussian white noise cannot yield desired logic behavior. Fortunately, LSR can also be expected by adjusting the correlation time of Gaussian colored noise. It can also be observed that the reliable region in the parameter plane of potential depth parameter a and multiplicative noise strength Q is small for the case of Gaussian white noise and it becomes larger with the increasing of noise color.