分数阶非对称耦合系统在对称周期势中的定向输运

摘要

在没有外力且周期势对称的情况下，对非对称耦合粒子链的运动，以具备更强刻画能力的分数阶微积分理论建立了分数阶模型，对其定向输运现象进行针对性研究，采用分数阶差分法进行数值求解并分析系统参数对定向输运速度的影响。相应仿真表明，分数阶非对称耦合系统在没有外力和噪声驱动的情况下仍能产生定向输运，且输运速度随阶数的增大而增大；当阶数固定时，粒子链平均速度随耦合强度和势垒高度非单调变化；当系统存在噪声时，粒子链平均速度出现了广义随机共振现象，且通过调节其他参数，可使得系统对噪声免疫甚至使噪声促进定向输运。%Based on the fractional calculus theory, in the absence of external driving force, the fractional transport model of asymmetric coupling particle chain in symmetric periodic potential is established. Using the method of fractional difference, the model is solved numerically and the influences of the various system parameters on directional transport velocity are discussed. Numerical results show that in the case without external force and noise-driven, the fractional asymmetric coupling system can still generate directional transport, and the transport velocity increases as fractional order increases. When the fractional order is fixed, the average velocity of the particle chain varies non-monotonically with coupling strength and barrier height. In the case with noise, the generalized stochastic resonance phenomenon occurs. Besides, we can make the noise not affect the system or even promote directional transport by adjusting other parameters.