具有人口统计随机性的持续随机游动中的反应前沿
Reaction fronts in persistent random walks with demographic stochasticity
摘要：
标准的反应扩散（RD）系统的特点是无限的速度和没有持久性的运动的个人，两个条件时，违反考虑活的有机体。在这里，我们考虑一个离散粒子模型，其中个人移动的持续随机行走有限的速度和增长的逻辑动力学。我们发现，当个体的数量是非常大的，基于个人的模型是很好地描述了连续反应Cattaneo方程（RCE），但对于较小的承载能力的值重要的有限人口效应出现。波动对传播速度的影响进行了研究，考虑RCE与截止的反应项，并通过数值模拟的个人为基础的模型。最后，一个更一般的Lévy步行过程中的个人的运输进行检查，并提出了所产生的行波的前速度的表达式。
英文摘要：
Standard Reaction-Diffusion (RD) systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle model in which individuals move following a persistent random walk with finite speed and grow with logistic dynamics. We show that when the number of individuals is very large, the individual-based model is well described by the continuous Reactive Cattaneo Equation (RCE), but for smaller values of the carrying capacity important finite-population effects arise. The effects of fluctuations on the propagation speed are investigated both considering the RCE with a cutoff in the reaction term and by means of numerical simulations of the individual-based model. Finally, a more general Lévy walk process for the transport of individuals is examined and an expression for the front speed of the resulting traveling wave is proposed.
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