中文摘要：

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。

英文摘要：

In this paper, a spatiotemporally asymmetric fractional Langevin-like ratchet is constructed for the operation of a one-dimensional linear molecular motor subjected to both temporally asymmetric unbiased Langevin-like noise generated by the Logistic mapping and spatially asymmetric periodic potential. In this ratchet, the Langevin-like noise is used to describe fluctuations of intracellular surrounding, and the fractional order is responsible for the effect of the non-ideal intracellular surrounding. Then, by deducing the corresponding discrete mapping, dependance of ratchet effect on parameters are numerically investigated. Numerical results show that both the temporal asymmetry of noise and the spatial asymmetry of potential are crucial to the directed-transport of the ratchet, and competitive spatially asymmetric potential can even reverse the unidirected transport generated by the temporally asymmetric noise at suitable parameters.