基于比率的Holling-Tanner干扰扩散系统的周期解

J4 ›› 2010, Vol. 48 ›› Issue (1): 45-49.

基于比率的Holling-Tanner干扰扩散系统的周期解

雷鸣

北华大学数学学院, 吉林吉林 132013

收稿日期:2009-06-23 出版日期:2010-01-26 发布日期:2010-01-27
通讯作者: 雷鸣 E-mail:bhdxlm@163.com.

Periodic Solution of Diffusive and Mutual InterferenceHolling-Tanner System with Ratio-Dependence

LEI Ming

College of Mathematics, Beihua University, Jilin 132013, Jilin Province, China

Received:2009-06-23 Online:2010-01-26 Published:2010-01-27
Contact: LEI Ming E-mail:bhdxlm@163.com.

摘要/Abstract

摘要：

利用重合度理论中的延拓定理, 讨论具有比率依赖和时滞的Holling-Tanner干扰扩散系统全局正周期解的存在性, 得到了保证周期解存在的充分条件. 结果表明，当食饵种群的內禀增长率大于其总消耗率时系统将产生生物性周期振荡.

关键词: Holling-Tanner系统, 干扰和扩散, 重合度理论, 正周期解

Abstract:

Using a continuation theorem based on Gaines and Mawhin’s coincidence degree, we studied the global existence of positive periodic solutions of a predatorprey diffusive system with mutual interference and ratio dependence. A set of easily verifiable sufficient conditions were obtained, which improved some known results. The results show when the prey population intrinsic increasing rate is greater than the total consumption rate, the system will bring periodic oscillation of biological nature.

Key words: HollingTanner system, diffusive and mutual interference, coincidence degree theory, positive periodic solution

中图分类号:

O175.14

雷鸣. 基于比率的Holling-Tanner干扰扩散系统的周期解[J]. J4, 2010, 48(1): 45-49.

LEI Ming. Periodic Solution of Diffusive and Mutual InterferenceHolling-Tanner System with Ratio-Dependence[J]. J4, 2010, 48(1): 45-49.

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