| 一类捕食者具有传染病的时滞生态模型 |
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| 引用本文： | 吴慧娟,宋 强. 一类捕食者具有传染病的时滞生态模型[J]. 信阳师范学院学报(自然科学版), 2014, 0(1): 8-11 |
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| 作者姓名： | 吴慧娟 宋 强 |
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| 作者单位： | ;1.信阳师范学院数学与信息科学学院;2.信阳水利技工学校;3.信阳职业技术学院数学与计算机科学系 |
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| 摘 要： | 研究了一类捕食者内部传播疾病且带时滞的捕食系统.分析了非负不变集、边界平衡态和正平衡态.当时滞τ足够小时,无病平衡点和正平衡点是局部渐近稳定的,随着时滞的增加,将产生Hopf分支.
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| 关 键 词： | 捕食模型,传染病模型 时滞 Hopf分支 |
Analysis of a Delayed Predator-prey Model with Disease in the Predator |
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| Affiliation: | ,College of Mathematics and Information Science,Xinyang Normal University,Department of Mathematics,Xinyang Technical School of Water Conservancy,College of Mathematics and Computer Science,Xinyang Vocational and Technical College |
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| Abstract: | A system of delayed functional differential equations was proposed as a predator-prey model with disease in the predator. The invariance of non-negativity,nature of boundary equilibria and the positive equilibrium were analyzed. It was showed that the disease-free and the positive equilibrium are locally asymptotically stable when time delayτ is suitable small,while a loss of stability by a Hopf bifurcation can occur as the delays increase. |
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| Keywords: | predator-prey model epidemic model delay hopf bifurcation |
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