| 一类具有非线性发生率的生态-流行病模型分析 |
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| 引用本文： | 刘宣亮,江文超. 一类具有非线性发生率的生态-流行病模型分析[J]. 北华大学学报(自然科学版), 2016, 17(3): 281-289. DOI: 10.11713/j.issn.1009-4822.2016.03.001 |
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| 作者姓名： | 刘宣亮 江文超 |
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| 作者单位： | 华南理工大学数学学院,广东 广州,510640;华南理工大学数学学院,广东 广州,510640 |
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| 基金项目： | 国家自然科学基金项目(11572127) |
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| 摘 要： | 对仅在捕食者中传播且具有非线性发生率的一类生态-流行病进行了研究.考虑了系统解的有界性、边界平衡点与正平衡点的存在条件及稳定性;利用分支理论与方法讨论了正平衡点的Bogdanov-Takens分支产生的条件,得到了相应的鞍结点分支曲线、Hopf分支曲线和同宿分支曲线;对正平衡点的Hopf分支,讨论了分支的方向及稳定极限环的存在性.
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| 关 键 词： | 生态-流行病模型 非线性发生率 稳定性 分支 |
Analysis of an Eco-Epidemiological Model with a Nonlinear Incidence Rate |
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| Liu Xuanliang,Jiang Wenchao. Analysis of an Eco-Epidemiological Model with a Nonlinear Incidence Rate[J]. Journal of Beihua University(Natural Science), 2016, 17(3): 281-289. DOI: 10.11713/j.issn.1009-4822.2016.03.001 |
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| Authors: | Liu Xuanliang Jiang Wenchao |
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| Abstract: | An eco-epidemiological model with a nonlinear incidence rate in the predator is considered. We analyze the boundedness of solutions and stability of equilibria. By using bifurcation methods and techniques,we study the Bogdanov-Takens bifurcation near a positive equilibrium,and obtain a saddle-node bifurcation curve,a Hopf bifurcation curve and a homoclinic bifurcation curve. The direction of Hopf bifurcation and the existence of a stable limit cycle near a positive equilibrium are also discussed. |
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| Keywords: | eco-epidemiological model nonlinear incidence rate stability bifurcation |
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