涨落作用下周期驱动的分数阶过阻尼棘轮模型的混沌输运现象

Chaotic transport of fractional over-damped ratchet with fluctuation and periodic drive

考虑涨落作用下周期驱动的过阻尼分数阶棘轮模型,通过模型的数值求解,研究确定性棘轮的混沌特性与噪声的作用对输运行为的影响,进而讨论过阻尼分数阶分子马达反向输运的机理.分析表明:随着势垒高度、势不对称性与模型记忆性的变化,随机棘轮的反向输运并不必然地要求确定性棘轮也反向输运;随着模型阶数的减小,亦即分数阻尼介质记忆性的增强,确定性棘轮在反向输运之前会经历一个周期倍化导致的混沌状态,但在噪声作用下,反向流的发生会提前,即混沌状态的确定性棘轮在噪声的作用下即可进行反向输运.也就是说,噪声能定性地改变棘轮的输运状态:从无噪声时的混沌运动到有噪声时的定向输运.这是过阻尼随机棘轮反向输运的一种机理,也是噪声在定向输运过程中发挥积极作用的一个体现.

The fractional over-damped ratchet model with thermal fluctuation and periodic drive is introduced by using the damping kernel function of general Langevin equation in the form of power law based on the assumption that cytosol in biological cells has characteristics of power-law memory. On basis of the Grunwald-Letnikov definition of fractional derivative, the numerical solution of this ratchet model is obtained. And furthermore, according to the numerical solution, the transport behaviors of stochastic ratchet and corresponding deterministic ratchet （especially when the deterministic ratchet has chaotic trajectory） are investigated, based on which we try to analyze how chaotic properties of the deterministic ratchet and the actions of noise influence the transport properties of molecular motors and moreover find the possible mechanism of current reversal of fractional molecular motor. Numerical results show that, as barrier height, barrier asymmetry and memorability of model change, the current reversal in deterministic ratchet is not necessarily required to appear when happening indeed in corresponding stochastic ratchet; moreover, with the decrease of order p, there exists a chaotic regime in deterministic ratchet model before current reversal, but with the disturbance of noise, current reversal will happen more earlier, namely, chaotic current direction in deterministic ratchet model can be reversed when disturbance of noise exists. This also demonstrates that noise can essentially change the transport behavior of a ratchet; current can change from chaotic state in a ratchet with no noise to directed transport with noise. This is a possible mechanism of current reversal of a fractional stochastic ratchet, and also a reflection that noise plays an active role in directed transport.