| 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. 首先分析了模型的适定性 (存在性、唯一性和正性) 和半平凡常数稳态解的稳定性. 接着又分析了正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. 最后利用数值模拟验证所得结论. |
| 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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zhouxinyan
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School of Mathematics and Statistics, Southwest University
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| Abstract: |
| This paper investigates a predator-prey model with memory delay under Neumann boundary conditions. Firstly, the well posedness (existence, uniqueness, and positivity) of the model and the stability of the semi-trivial constant steady-state solution are analyzed. Then, the stability of the positive constant steady-state solution is analyzed. At the same time, the Turing bifurcation and Hopf bifurcation of the system are obtained by using memory-based diffusion coefficient as the bifurcation parameter. Finally, numerical simulations are used to verify the conclusions obtained. |
| Key words: Reaction-diffusion equation Memory delay Well-posedness Turing bifurcation Hopf bifurcation |
