论文标题
离散随机双方方程的行驶波
Travelling waves for discrete stochastic bistable equations
论文作者
论文摘要
许多物理，化学和生物系统具有固有的离散空间结构，会强烈影响其动力学行为。类似的说明适用于内部或外部噪声，以及非本地耦合。在本文中，我们研究了非局部空间离散化和随机扰动对Nagumo方程中的行进波的综合作用，这是BISCAble Reaction-Reaction-Reaction-Reaction-Rection-Rection-eartial partiale方程（PDES）的典型模型。我们证明，在适当的参数条件下，Nagumo方程的各种离散性变体具有解决方案，如果噪声水平和空间离散化足够小，则可以长时间与经典单调Nagumo前部保持近距离。
Many physical, chemical and biological systems have an inherent discrete spatial structure that strongly influences their dynamical behaviour. Similar remarks apply to internal or external noise, as well as to nonlocal coupling. In this paper we study the combined effect of nonlocal spatial discretization and stochastic perturbations on travelling waves in the Nagumo equation, which is a prototypical model for bistable reaction-diffusion partial differential equations (PDEs). We prove that under suitable parameter conditions, various discrete-stochastic variants of the Nagumo equation have solutions, which stay close on long time scales to the classical monotone Nagumo front with high probability if the noise level and spatial discretization are sufficiently small.
