Stochastic resonance in an over-damped linear oscillator

For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function,we study the stochastic resonance(SR) in this paper. Using the Shapiro–Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio(SNR). Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.     

空时非对称分数阶类Langevin棘齿

研究了空时非对称分数阶类Langevin分子马达棘齿模型,其中势函数是空间对称破缺的周期势,时间非对称类Langevin噪声由Logistic映射生成,而分数阶则刻画了分子马达工作环境的非理想程度.通过将模型转化为离散映射,即研究其整时间点情形,数值模拟了噪声的时间非对称性、势函数的空间非对称性以及分数阶对模型定向输运行为的影响.数值模拟结果表明:噪声的时间非对称性是定向流产生的根源,而势函数的空间非对称性能够与其进行竞争与协作,并在适当的参数条件下导致定向流的逆转;分数阶仅影响定向流的大小而不改变其方向.与经典的整数阶分子马达模型或时间非对称分数阶分子马达棘齿模型相比,该模型可以更为真实地描述分子马达的噪声整流工作机理.     

时间非对称分数阶类Langevin棘齿

本文将细胞内环境假定为分数阶牛顿黏弹性体并建立了单位质量的一维线动分子马达的时间非对称分数阶类郎之万棘齿模型,其中的周期势函数是空间对称的,而用于刻画ATP水解反应引起的环境波动的则是无偏的时间非对称类郎之万噪声.然后本文将模型转化为离散映射以便进行计算机模拟.最后本文以Logistic映射所生成的类郎之万噪声为例简单模拟了模型的定向输运行为.各参数情形下的模拟结果均显示:无需势函数的空间对称破缺,时间非对称的类郎之万噪声已足以引起模型的定向输运.负向的输运行为应归因于Logistic映射的两个不稳定不动点的非对称分布.因此,尽管模拟结果同整数阶模型相比并无本质区别,但分数阶模型对于分子马达的噪声整流机理的刻画却无疑更接近实际情况.     

分数阶双头分子马达的欠扩散输运现象

研究具有幂律记忆性的细胞液中双头分子马达的定向输运现象,选取幂函数作为广义Langevin方程的阻尼核函数,建立了分数阶过阻尼耦合Brown马达模型,讨论了阶数及耦合系数对双头分子马达定向输运速度的影响. 仿真结果表明,分数阶过阻尼双头分子马达也会产生定向输运现象,并且在某些阶数下会产生整数阶情形所不具有的反向定向流. 当噪声强度固定时,输运速度随着阶数以及耦合系数的变化均会出现广义随机共振现象. 特别地,研究发现双头分子马达在记忆闪烁棘轮势中具有某些单头分子马达所不具备的运动特性,定向流的大小和方向由噪声与双头间作用力相互耦合控制. 关键词： 分数阶双头分子马达 欠扩散 定向输运 广义随机共振