| 捕食者和食饵均带有扩散的随机捕食-食饵模型动力学分析 |
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| 引用本文： | 祖力,黄冬冬,柳扬.捕食者和食饵均带有扩散的随机捕食-食饵模型动力学分析[J].应用数学和力学,2017,38(3):355-368. |
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| 作者姓名： | 祖力 黄冬冬 柳扬 |
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| 作者单位： | 1海南师范大学 数学与统计学院, 海口 571158;2大连大学 信息工程学院, 辽宁 大连 116600 |
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| 基金项目： | 海南省教育厅高等学校科学研究项目(Hjkj2013-16)，海南省自然科学基金(20161006) |
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| 摘 要： | 考虑了斑块环境下捕食者种群和食饵种群分别在n个斑块扩散的随机捕食 食饵模型.利用Lyapunov函数法证明了对任意给定的初始值,随机系统全局正解的存在唯一性,并对其进行了有界性分析.此外给出了食饵种群及整个系统灭绝的充分条件.最后通过数值模拟验证了所得理论的正确性.
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| 关 键 词： | 捕食-食饵模型 随机扰动 扩散 随机最终有界 灭绝性 |
| 收稿时间： | 2016-02-23 |
Dynamics of Dual-Dispersal Predator-Prey Systems Under Stochastic Perturbations |
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| ZU Li,HUANG Dong-dong,LIU Yang.Dynamics of Dual-Dispersal Predator-Prey Systems Under Stochastic Perturbations[J].Applied Mathematics and Mechanics,2017,38(3):355-368. |
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| Authors: | ZU Li HUANG Dong-dong LIU Yang |
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| Institution: | 1School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P.R.China;2College of Information Engineering, Dalian University, Dalian, Liaoning 116600, P.R.China |
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| Abstract: | A predator-prey model was considered,in which both the predators and the preys dispersed among n patches under stochastic perturbations.Based on the method of Lyapunov functions,it was proved that a unique global positive solution existed for any given positive initial value;in turn,the property of ultimate boundedness was obtained.In addition,the sufficient conditions for the extinctions of the preys and even the whole system were given.Finally,the theoretic conclusions were validated by numerical simulations. |
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| Keywords: | predator-prey model stochastic perturbation dispersal stochastically ultimate boundedness extinction |
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