| 一类具有强食饵和弱食饵的捕食系统分析 |
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| 作者单位： | ;1.山西师范大学数学与计算机科学学院 |
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| 摘 要： | 提出并研究了一类具有两个相互竞争的食饵种群与一个以这两个物种为食的捕食者种群的捕食系统.首先通过比较原理研究了该系统解的正有界性及系统平衡点的存在性,并运用特征值方法对可能存在的平衡点的局部渐近稳定性进行了讨论.其次利用微分方程的基本理论,得到了系统持久性的充分条件.然后通过构造Lyapunov函数讨论了系统平衡点的全局稳定性.最后,利用数值模拟验证本文的主要结论.
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| 关 键 词： | 捕食系统 平衡点 稳定性 持久性 |
Analyses of a Class of Predator,Weaker Prey and Stronger Prey System |
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| Affiliation: | ,School of Mathematics and Computer Science,Shanxi Normal University |
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| Abstract: | The dynamics of a predator-prey system consisting of two competitive prey populations and one predator population,which feeds on both the prey species,were studied.Firstly,the positivity and boundedness of the solutions and the existence of all the possible equilibria of this system were investigated.Further,by using qualitative method of ordinary differential equation,the local asymptotically stability of equilibria and the persistence of the system were discussed.The global asymptotic stability of the positive equilibrium was obtained by constructing Lyapunov function.Finally,the numerical analyses were given to show the effectiveness of the main results. |
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| Keywords: | predator-prey system equilibria stability analysis persistence |
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