具有扩散项的互惠–寄生耦合模型图灵斑图研究

Analysis of Spatial Pattern in Mutualistic-Parasitic Coupled System with Diffusion

摘要: 本文将扩散因子引入互惠–寄生耦合系统，建立互惠–寄生耦合空间模型，研究其斑图动力学性态。利用斑图理论，给出耦合系统产生Hopf分支和Turing分支的临界表达式，并由此确定出图灵斑图出现的参数区域，运用有限差分法模拟模型的斑图结构。结果表明，当扩散存在时互惠–寄生耦合系统具有黑眼(点状)斑图结构，寄生物在空间呈现孤立的高密度分布。

Abstract: In this paper, we establish mutualistic-parasitic coupled spatial model incorporating diffusion, and study the dynamical behaviors of this spatial model. By spatial pattern theory, we obtain the conditions for Hopf bifurcation and Turing bifurcation, and give the exact parameter space for Turing domain. By utilizing difference approximation method, we find that the spatial model ex-hibits black eye spotted pattern, which shows that the diffusion can result in an isolated high den-sity of parasite in the space.