| 一类具有Watt型功能性反应的捕食系统的极限环与稳定性 |
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| 引用本文： | 程荣福,王卓.一类具有Watt型功能性反应的捕食系统的极限环与稳定性[J].大学数学,2009,25(2). |
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| 作者姓名： | 程荣福 王卓 |
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| 作者单位： | 北华大学,吉林,吉林,132021 |
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| 摘 要： | 研究一类具有Watt型功能性反应的捕食模型.讨论了该系统正平衡点的存在性以及非负平衡点的性态,应用Poincare-Bendixson定理和张芷芬定理,证明了极限环的存在性和唯一性,并采用构造Dulac函数的方法,获得了正平衡点全局渐近稳定性的一个充分条件.
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| 关 键 词： | 捕食系统 Watt型功能性反应 正平衡点 极限环 稳定性 |
The Stability and Limit Cycles of a Class Predator-prey System with Watt Type Functional Response |
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| CHENG Rong-fu,WANG Zhuo.The Stability and Limit Cycles of a Class Predator-prey System with Watt Type Functional Response[J].College Mathematics,2009,25(2). |
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| Authors: | CHENG Rong-fu WANG Zhuo |
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| Institution: | Beihua University;Jilin 132021;China |
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| Abstract: | A class of predator-prey model with Watt type functional response is studied.The existence of positive equilibrium point and the properties of non-negative equilibrium points are discussed.It proves the existence and uniqueness of limit cycles applying the Poincare-Bendixson theorem and Zhang Zhifen theorem.With the methods of constructing Dulac function,it obtains an ample factor of positive equilibrium points global asymptotic stability. |
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| Keywords: | predator-prey system Watt type functional response positive equilibrium points limit cycles stability |
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