带反馈的分数阶耦合布朗马达的定向输运

研究具有幂律记忆性的带反馈耦合布朗马达的定向输运现象, 引入分数阶理论, 建立了带反馈的分数阶耦合布朗马达模型, 利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响. 仿真结果表明, 系统的记忆性通过影响带反馈的棘齿势的打开和闭合而影响粒子的定向输运, 即当系统的阶数在较小的范围内, 系统的记忆性会使带反馈的棘齿势的开关频率增加, 从而增大定向流速; 当系统其他参数(势垒高度、噪声强度等)固定时, 输运速度随着阶数的变化出现广义随机共振现象.

Transport properties of fractional coupled Brownian motors in ratchet potential with feedback

Based on the theory of fractional integration, direct transport behaviors of coupled Brownian motors with feedback control in viscoelastic media are investigated. The mathematical model of fractional overdamped coupled Brownian motors is established by adopting the power function as damping kernel function of general Langevin equation due to the power-law memory characteristics of cytosol in biological cells. Numerical solution is observed by fractional difference method and the influence of model parameters on cooperative direct transport of the coupled Brownian motors is discussed in detail by numerical simulation. The research shows that the memory of the fractional dynamical system can affect the direct transport phenomenon of the coupled Brownian motors through changing the on-off switching frequency of the ratchet potential with feedback control. To be more specific, in a proper range of the fractional order, the memory of the dynamical system can increase the on-off switching frequency of the ratchet potential, which can lead to the velocity increase of the direct transport. Furthermore, in the case of small fractional order, since the coupled Brownian motors move under the competition between the damping force with memory and the potential force with feedback control, the resultant force exerted on the coupled particles is always positive when the ratchet potential with feedback control is on although the fractional damping force is large, which leads to the result that the coupled Brownian motors move in the positive direction in the mass. On the contrary, in the case of large fractional order, the on-off switching frequency of potential with feedback control becomes small, as a result of which the main influential factor of the direct transport becomes the potential depth. Therefore the coupled Brownian motors are more likely to stay in the potential wells for a long time because the probability that describes the possibility that the coupled Brownian motors surmount the potential barriers becomes small. Finally, with the parameters of the fractional dynamical system (e.g. potential depth, noise intensity) fixed, the direct transport velocity of the coupled Brownian motors shows the generalized stochastic resonant phenomenon while the fractional order varies.