| 具有扩散现象的非自治四维生态流行病模型的稳定性分析 |
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| 引用本文： | 马成荣.具有扩散现象的非自治四维生态流行病模型的稳定性分析[J].北华大学学报(自然科学版),2011(2):137-143. |
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| 作者姓名： | 马成荣 |
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| 作者单位： | 浙江工业职业技术学院;上海大学数学系; |
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| 基金项目： | 浙江省教育厅科研项目(Y201018696,Y201019247) |
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| 摘 要： | 建立并分析了具有扩散现象的非自治四维生态流行病模型,得到了系统持久生存的充分条件;基于Brouwer不动点定理,证明了系统周期解的存在性,同时通过构造Lyapunov泛函得到该系统周期解的唯一性与全局渐近稳定性,并给出了合理的生态解释.最后,通过一个数值例子说明了结论的有效性.
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| 关 键 词： | 持久生存 周期解 全局渐近稳定 |
Stability Analysis for Four-Dimensional Nonautonomous and Eco-Epidemiological Model with Diffusion |
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| MA Cheng-rong.Stability Analysis for Four-Dimensional Nonautonomous and Eco-Epidemiological Model with Diffusion[J].Journal of Beihua University(Natural Science),2011(2):137-143. |
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| Authors: | MA Cheng-rong |
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| Affiliation: | MA Cheng-rong1,2(1.Zhejiang Industry Polytechnic College,Shaoxing 312000,China,2.Mathematics Department of Shanghai University,Shanghai 200444,China) |
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| Abstract: | A four-dimensional nonautonomous and eco-epidemiological model with diffusion is modified and analyzed.Sufficient conditions are obtained for the permanence of the eco-epidemiological model and the existence of the periodic solutions is proven by Brouwer Fixed Point Theorem.Moreover,some conditions for global asymptotic stability of the system are investigated by using Lyapunov function.Also,some rational explanations for the eco-epidemiological model from the point of ecology are given.A numerical example ... |
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| Keywords: | permanence periodic solution global asymptotic stability |
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