| 具有收获率和功能性反应的捕食系统的周期解存在性 |
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| 引用本文： | 傅金波,陈兰荪.具有收获率和功能性反应的捕食系统的周期解存在性[J].应用数学,2021,34(2):289-297. |
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| 作者姓名： | 傅金波 陈兰荪 |
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| 作者单位： | 1. 闽南科技学院, 福建 泉州 362332; 2. 中国科学院数学与系统科学研究院, 北京 100080 |
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| 基金项目： | 国家自然科学基金(11371306);福建省高等学校新世纪优秀人才支持计划(2018);泉州市科技计划项目(2018C094R);福建省2019省级线下一流本科课程(工程应用数学C)(SJKC-2019-01)。 |
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| 摘 要： | 根据种群动力学原理,考虑捕食者具有Hassell-Varley型功能性反应,建立了具有非线性收获率和功能性反应的捕食者-食饵的周期系统.利用微分方程比较原理,重合度理论中Gaines和Mawhin延拓定理,讨论了系统的一致持久性,建立了该系统至少存在一个正周期解的一套易于验证的充分条件.最后,通过数值模拟验证了结论的正确性.
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| 关 键 词： | 捕食系统 非线性收获率 Hassell-Varley型功能性反应 正周期解 |
| 收稿时间： | 2020/4/2 0:00:00 |
Existence of Periodic Solution of Predator-Prey System with Harvest Rate and Functional Response |
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| FU Jinbo,CHEN Lansun.Existence of Periodic Solution of Predator-Prey System with Harvest Rate and Functional Response[J].Mathematica Applicata,2021,34(2):289-297. |
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| Authors: | FU Jinbo CHEN Lansun |
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| Institution: | (Minnan Science and Technology Institute,Quanzhou 362332,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China) |
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| Abstract: | In this paper, according to the principle of population dynamics, the predator having a Hassell-Varley type functional response is considered and a class of predator-prey periodic system with nonlinear harvest rate and functional response is established. By applying Comparison Theorem of differential equation, Gaines and Mawhin’s Continuation Theorem of coincidence degree theory, we discussed consistent persistence of the system and established a set of easily verifiable sufficient conditions under which this system has at least exist one positive periodic solution. At last, the correctness of the conclusion is verified by numerical simulation. |
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| Keywords: | Predator-prey system Nonlinear harvest rate Hassell-Varley type functional response Positive periodic solution |
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