Fractional dynamics using an ensemble of classical trajectories
Fractional dynamics using an ensemble of classical trajectories
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使用经典轨迹集合的分数动力学
DOI：
10.1103/physreve.97.012132
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发表时间：
2018
影响因子：
2.4
通讯作者：
Zheng Yujun
中科院分区：
文献类型：
--
作者：
Sun Zhaopeng;Dong Hao;Zheng Yujun
提出了基于轨迹的分数动力学公式，并确定性地生成轨迹。在此理论框架中，我们根据汇合超几何函数 () 推导了一类新的估计量来表示 Riesz 分数阶导数。使用这种方法，自由和受限 Lévy 飞行的模拟与精确的数值和分析结果非常一致。此外，还研究了指数 Lévy 噪声驱动的双稳态电位中的势垒穿越。在相空间中，轨迹的行为更好地揭示了Lévy飞行的特征。
A trajectory-based formulation for fractional dynamics is presented and the trajectories are generated deterministically. In this theoretical framework, we derive a new class of estimators in terms of confluent hypergeometric function () to represent the Riesz fractional derivative. Using this method, the simulation of free and confined Lévy flight are in excellent agreement with the exact numerical and analytical results. In addition, the barrier crossing in a bistable potential driven by Lévy noise of indexis investigated. In phase space, the behavior of trajectories reveal the feature of Lévy flight in a better perspective.