论文标题
Lévy噪声驱动的逃离阿克坦潜在井
Lévy noise-driven escape from arctan potential wells
论文作者
论文摘要
从潜在的井中逃脱的是随机动力学系统研究中的原型问题，代表了从化学反应到离开运动生态学的既定家庭范围的现实情况。同时，l {é} Vy噪声是一种建模的模型系统的方法，其特征是统计异常值和较高阶段的差异，从基因表达控制到动物和人类的运动模式。在这里，我们研究了莱维噪声驱动的问题，这些问题逃脱了几乎矩形的，阿克丹势能受到两个吸收边界的限制。我们揭示了观察到的瞬态动力学的类比，即单孔电位中L {é} Vy过程的固定状态的一般特性。第一个逃生动力学显示出表现指数式尾巴。我们检查了逃脱对阿克坦电势的形状参数，陡度和高度的依赖性。最后，我们详细探讨了第一驱动时间和最后一个打点的概率密度的行为。
The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, L{é}vy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher-order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Lévy noise-driven escape from an almost rectangular, arctan potential well restricted by two absorbing boundaries. We unveil analogies of the observed transient dynamics to the general properties of stationary states of L{é}vy processes in single-well potentials. The first escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness and height, of the arctan potential. Finally, we explore in detail the behavior of the probability densities of the first-escape time and the last-hitting point.
