| 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.利用特征值法获得了非负常值平衡点的局部稳定性;通过构建合适的Lyapunov函数,推广了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 反应扩散方程 稳定性 Lyapunov函数 |
| DOI： |
| 分类号:O175 |
| 基金项目:国家自然科学基金项目资助(12426515). |
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| STABILITY ANALYSIS OF A CLASS OF ECOLOGICAL EPIDEMIC MODELS |
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LUO Wen-jing1,2, WANG Hui1, SU You-hui2
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1.School of Mathematics and Statistics, Yili Normal University, Yining 835000, China;2.School of Mathematics and Statistics, Xuzhou Institute of Technology, Xuzhou 221018, China
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| Abstract: |
| In this paper, the stability of a class of ecoepidemiological model solutions with diffusion terms is studied. The eigenvalue method was used to obtain 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 generalized, and finally, the global stability of the total 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 equation stability Lyapunov function |
