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| 摘要: |
| 本文研究了一类在Neumann边界条件下带有记忆时滞的捕食者-食饵模型稳定性以及分支的相关问题.利用强极大值原理和抛物方程的比较原理得到了模型的适定性(存在性、唯一性和正性),然后分析了系统中常数稳态解的稳定性;同时以基于记忆的扩散系数为分支参数,得到了系统的Turing分支和Hopf分支;说明了在该系统中对于任意的记忆时滞,总会存在大于临界值的记忆扩散系数, 使得正常数稳态解是不稳定的;最后利用数值模拟验证相应结论. |
| 关键词: 反应-扩散方程 记忆时滞 适定性 Turing分支 Hopf分支 |
| DOI： |
| 分类号:O175 |
| 基金项目: |
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| BIFURCATION ANALYSIS OF A PREDATOR-PREY MODEL WITH MEMORY DELAY |
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ZHOU Xin-yan,WANG Xiao-li
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| Abstract: |
| In this paper, we study the stability and bifurcation issues of a predator-prey model with memory delay under Neumann boundary conditions. The strong maximum principle and the comparison principle of parabolic equations are used to obtain the well-posedness of the model (existence, uniqueness and positivity), and then the stability of the constant steady-state solution in the system is analyzed. At the same time, the Turing bifurcation and Hopf bifurcation of the system are obtained by taking the memory-based diffusion coefficient as the bifurcation parameter; it is shown that for any memory delay in this system, there will always be a memory diffusion coefficient greater than the critical value, making the positive constant steady-state solution unstable. Finally, the numerical simulation is used to verify the corresponding conclusion. |
| Key words: reaction-diffusion equation memory delay well-posedness Turing bifurcation Hopf bifurcation |
