| 一类两种群均有收获率捕食系统的细焦点与极限环 |
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| 引用本文： | 韩二东,郑唯唯,罗立贵.一类两种群均有收获率捕食系统的细焦点与极限环[J].生物数学学报,2012(3):447-454. |
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| 作者姓名： | 韩二东 郑唯唯 罗立贵 |
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| 作者单位： | 西安工程大学理学院,陕西西安710048 |
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| 基金项目： | 陕西省教育厅自然科学基金资助项目（11JK0502）; 西安工程大学博士科研启动基金 |
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| 摘 要： | 研究一类具有HollingⅡ类功能反应且两种群均为非常数收获率的捕食系统,其中食饵种群具有非线性密度制约.利用微分方程定性与稳定性理论及分支理论,得到系统平衡点的性态及极限环存在与否的充分条件,利用Hopf分支理论得到存到多个极限环的充分条件.
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| 关 键 词： | 收获率 非线性密度制约 细焦点 极限环 |
Weak Focus and Limit Cycles of a Predator-prey System with Harvesting Rates |
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| HAN Er-dong,ZHENG Wei-wei,LUO Li-gui.Weak Focus and Limit Cycles of a Predator-prey System with Harvesting Rates[J].Journal of Biomathematics,2012(3):447-454. |
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| Authors: | HAN Er-dong ZHENG Wei-wei LUO Li-gui |
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| Institution: | (School of Science,Xi＇an Polytechnic University,Xi＇an Shanxi 710048 China) |
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| Abstract: | A kind of predator-prey system with outstanding harvesting rates under HollingⅡfunctional response is considered,where prey is nonlinear density dependent.Using ordinary differential equations characterization,stability and bifurcation theory,the behavior of equilibrium points and sufficient conditions of the existence of the limit cycles are given.Meanwhile, on the basis of the Hopf-bifurcations,some sufficient conditions are obtained for the existence of several limit cycles. |
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| Keywords: | harvesting rate Nonlinear density dependent Weak focus Limit cycle |
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