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| 摘要: |
| 本文研究了一类带有扩散项的生态流行病模型解的稳定性问题. 在齐次Neumann边界条件下，利用特征值法讨论了非负常值平衡点的局部稳定性；通过构建合适的Lyapunov函数，证明了在适当参数条件下半共存平衡点和全共存平衡点的全局稳定性，最后，用数值模拟验证了全共存平衡点的全局稳定性.本研究为理解疾病在生态系统中的调控作用提供了数学理论支持. |
| 关键词: 捕食系统 生态流行病模型 反应扩散 稳定性 Lyapunov函数 |
| DOI： |
| 分类号:O175 |
| 基金项目:国家自然科学基金资助项目（12426515） |
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| Stability analysis of a class of ecological epidemic models |
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luowenjing,Wang Hui
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| Abstract: |
| In this paper, the stability of a class of ecological epidemic model’s solutions with diffusion terms is studied. Under the homogeneous Neumann boundary condition, the eigenvalue method is used to discuss the local stability of the non-negative constant equilibrium point. By constructing a suitable Lyapunov function, the global stability of the semi-coexistence equilibrium point and the full coexistence equilibrium point is proved under the appropriate parameter conditions, and finally, the global stability of the full coexistence equilibrium point is verified by numerical simulation. This study provides mathematical support for understanding the regulatory role of disease in the ecosystem. |
| Key words: Predatory system Ecological epidemic model Reaction diffusion Stability Lyapunov function |
