Brown S, Dockery J, Pernarowski M
Mathematics Department, Humboldt State University, Arcata, CA 95521, United States.
Math Biosci. 2005 Mar;194(1):21-36. doi: 10.1016/j.mbs.2004.10.001.
Presented is a reaction-diffusion model for the interaction of pioneer and climax species. For certain parameters the system exhibits bistability and traveling wave solutions. Specifically, we show that when the climax species diffuses at a slow rate there are traveling wave solutions which correspond to extinction waves of either the pioneer or climax species. A leading order analysis is used in the one-dimensional spatial case to estimate the wave speed sign that determines which species becomes extinct. Results of these analyses are then compared to numerical simulations of wave front propagation for the model on one and two-dimensional spatial domains. A simple mechanism for harvesting is also introduced.
本文提出了一个先锋物种和顶极物种相互作用的反应扩散模型。对于某些参数，该系统呈现双稳性和行波解。具体而言，我们表明，当顶极物种以缓慢速率扩散时，存在对应于先锋物种或顶极物种灭绝波的行波解。在一维空间情形下，采用主导阶分析来估计决定哪个物种灭绝的波速符号。然后将这些分析结果与该模型在一维和二维空间域上波前传播的数值模拟结果进行比较。还引入了一种简单的收获机制。
