| 食饵和捕食者均染病的捕食-被捕食模型的分析 |
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| 作者单位： | ;1.河南师范大学数学与信息科学学院;2.河南师范大学优化控制河南省工程实验室;3.河南师范大学新联学院 |
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| 摘 要： | 讨论一个食饵种群和捕食者种群同时感染疾病的捕食-被捕食模型,且考虑了由捕食者妊娠期引起的时滞.通过分析特征方程,得到了平衡位置的局部稳定和出现Hopf分支的条件,并且由此给出了食饵或者捕食者种群灭绝的阈值条件以及种群内部疾病的基本再生数;利用比较定理,研究了边界平衡位置的全局稳定性.
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| 关 键 词： | 捕食-被捕食模型 时滞 Hopf分支 全局渐近稳定性 再生数 |
A Predator-prey Model with Disease in Prey and Predator |
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| Institution: | ,College of Mathematics and Information Science,Henan Normal University,Henan Engineering Laboratory of Big Data Statistical Analysis and Optical Control,Henan Normal University,College of Xinlian,Henan Normal University |
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| Abstract: | In this paper,we discuss a predator-prey model with populations affected by disease and the time delay caused by pregnant period of predator population is considered.By analyzing the characteristic equation,sufficient conditions are derived for the local stability and Hopf bifurcation of the boundary equilibria,thus,threshold conditions of extinction for prey and predator populationsand the basic reproductive number of disease for populations can be obtained.By comparison theorem,criterion is established for the global stability of some boundary equilibria. |
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| Keywords: | predator-prey model time delay Hopf bifurcation global asymptotic stability the reproductive number |
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