Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction
Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction
复制标题
DOI：
10.1093/imamat/68.4.409
复制
发表时间：
2003-08
影响因子：
1.2
通讯作者：
P. Weng;Huaxiong Huang;Jianhong Wu
中科院分区：
文献类型：
--
作者：
P. Weng;Huaxiong Huang;Jianhong Wu
本文建立了一维斑块环境中单种群的格点模型，该环境中有无穷多个斑块通过扩散局部连通。在成熟种群的死亡率和扩散率与年龄无关的假设下，证明了成熟种群的动力学行为是由一个具有全局相互作用的格点时滞微分方程控制的.我们研究了初值问题的适定性，得到了当波速c > c * 时单调行波的存在性。我们证明了最小波速c * 也是传播的渐近速度，它单调地依赖于成熟种群的成熟期和扩散率。
In this paper, we derive a lattice model for a single species in a one-dimensional patchy environment with infinite number of patches connected locally by diffusion. Under the assumption that the death and diffusion rates of the mature population are age independent, we show that the dynamics of the mature population is governed by a lattice delay differential equation with global interactions. We study the well-posedness of the initial-value problem and obtain the existence of monotone travelling waves for wave speeds c > c * . We show that the minimal wave speed c * is also the asymptotic speed of propagation, which depends on the maturation period and the diffusion rate of mature population monotonically.