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

祖力; 黄冬冬; 柳扬

doi:10.21656/1000-0887.370051

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

doi: 10.21656/1000-0887.370051

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

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）

详细信息

作者简介:
祖力(1979—)，女，副教授，博士（E-mail: 147362868@qq.com）;黄冬冬(1990—)，男，硕士生（通讯作者. E-mail: 649078137@qq.com）;柳扬(1979—)，女，讲师，博士生.

中图分类号: O175.1
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出版历程
- 收稿日期: 2016-02-23
- 修回日期: 2016-10-16
- 刊出日期: 2017-03-15

Dynamics of Dual-Dispersal Predator-Prey Systems Under Stochastic Perturbations

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

摘要

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.
- 捕食-食饵模型 /
- 随机扰动 /
- 扩散 /
- 随机最终有界 /
- 灭绝性
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.
- predator-prey model /
- stochastic perturbation /
- dispersal /
- stochastically ultimate boundedness /
- extinction

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参考文献(16)

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