具Hassell-Varley-Holling反应非自治捕食者-食饵系统的动力学分析

数学物理学报 ›› 2011, Vol. 31 ›› Issue (5): 1295-1310.

具Hassell-Varley-Holling反应非自治捕食者-食饵系统的动力学分析

钟敏玲|刘秀湘

广东外语外贸大学信息科学技术学院广州 510006；华南师范大学数学科学学院广州 510631

收稿日期:2009-09-11 修回日期:2010-10-08 出版日期:2011-10-25 发布日期:2011-10-25
基金资助:
国家自然科学基金(10801056, 10971057)、广东省自然科学基金(8451063101000730)和教育部博士点专项基金(20094407110001)资助

Dynamical Analysis of a Predator-prey System with Hassell-Varley-Holling Functional Response

ZHONG Min-Ling, LIU Xiu-Xiang

School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006；School of Mathematical Sciences, South China Normal University, Guangzhou 510631

Received:2009-09-11 Revised:2010-10-08 Online:2011-10-25 Published:2011-10-25
Supported by:
国家自然科学基金(10801056, 10971057)、广东省自然科学基金(8451063101000730)和教育部博士点专项基金(20094407110001)资助

摘要/Abstract

摘要：

该文研究了具Hassell--Varley--Holling功能性反应的非自治系统.对一般非自治情形, 研究了种群的持续生存和绝灭性.对于周期(概周期)情形, 利用一个新的估计技巧和同伦不变性, 得到了周期解(概周期解)存在的充要条件, 同时研究了边界周期解(概周期解)的动力学行为. 最后通过数值例子说明所得结论并给出了一些仍待研究的问题.

关键词: Hassell--Varley--Holling功能性反应, 捕食者-食饵系统, 持续生存, 绝灭性, 周期解, 概周期解

Abstract:

This paper deals with a non-autonomous predator-prey system with Hassell-Varley-Holling functional response. The permanence and extinction are considered for general non-autonomous case. For periodic (almost periodic) case, necessary and sufficient criteria for the existence of positive periodic (almost periodic) solutions are derived by a new estimation technique and the invariance property of homotopy, the dynamics of boundary periodic (almost periodic) solutions are also investigated. The authors end this paper with some numerical simulations and interesting problems remaining.

Key words: Hassell-Varley-Holling functional response, Predator-prey system, Permanence, Extinction, Periodic solution, Almost periodic solution

中图分类号:

34C60

钟敏玲, 刘秀湘. 具Hassell-Varley-Holling反应非自治捕食者-食饵系统的动力学分析[J]. 数学物理学报, 2011, 31(5): 1295-1310.

ZHONG Min-Ling, LIU Xiu-Xiang. Dynamical Analysis of a Predator-prey System with Hassell-Varley-Holling Functional Response[J]. Acta mathematica scientia,Series A, 2011, 31(5): 1295-1310.

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