[1]汪东树,王全义.一类具时滞和比率的扩散系统正周期解[J].华侨大学学报(自然科学版),2006,27(4):358-361.[doi:10.3969/j.issn.1000-5013.2006.04.006]
　Wang Dongshu,Wang Quanyi.Existence of Periodic Solution for Predator-Prey Diffusive System of Two Species with Time Delay and Ratio[J].Journal of Huaqiao University(Natural Science),2006,27(4):358-361.[doi:10.3969/j.issn.1000-5013.2006.04.006]
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一类具时滞和比率的扩散系统正周期解()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第27卷
期数:
2006年第4期
页码:
358-361
栏目:
出版日期:
2006-10-20

文章信息/Info

Title:
Existence of Periodic Solution for Predator-Prey Diffusive System of Two Species with Time Delay and Ratio
文章编号:
1000-5013(2006)04-0358-04
作者:
汪东树; 王全义
华侨大学数学系; 华侨大学数学系 福建泉州362021; 福建泉州362021
Author(s):
Wang Dongshu;  Wang Quanyi
Department of Mathematics, Huaqiao University, 362021, Quanzhou, China
关键词:
时滞;  比率;  重合度;  周期解
Keywords:
time-delay;  ratio;  coincidence degree;  periodic solution
分类号:
O175.14
DOI:
10.3969/j.issn.1000-5013.2006.04.006
文献标志码:
A
摘要:
研究一类具有时滞和比率的,且有Machaelis-Menten型功能性反应的非自治两种群捕食者-食饵扩散系统,其中所有参数都是周期函数.系统由两种群及两斑块构成,食饵种群能够在两斑块间扩散,而捕食者种群被限制在某一斑块中.文中应用重合度理论中的延拓定理,结合分析技巧构造一个同伦变换,得出系统存在正周期解的充分条件,且这些条件与扩散系数是无关.
Abstract:
One class of nonautonomous two species predator-prey model with diffusion,time delays and Machaelis-Menten type functional response is studied with all parameters are periodic functions.The system,which is composed of two patches and two species,the prey can diffuse between two patches,but the predator is confined to one patch.By using some analysis techniques and the continuation theorem of coincidence degree theory and constructing a homotopy operator,we obtain some sufficient conditions which guarantee the existence of periodic solution of the system.In particularly,these conditions are not relevant to the diffusion coefficients.

参考文献/References:

[1] 董士杰, 葛渭高. 具时滞和基于比率的两种群捕食者-食饵系统的周期解 [J]. 应用数学学报, 2004(1):132-141.doi:10.3321/j.issn:0254-3079.2004.01.015.
[2] Li Biwen, Zeng Xianwu. Existence of positive solution for a two-patches competition system with diffusion and time delay and functional response [J]. Appl Math J Chin Univ Ser (B), 2003(1):1-8.
[3] Xu Rui, Chen Lansun. Persistence and stability for a two-species ratio-dependent predator-prey system with time delay in a two-patch environment [J]. Computers and Mathematics with Applications, 2000.577-588.
[4] Gaines R E, Mawhin J L. Coincidence degree and nonlinear differential equations [M]. Berlin:Springer-Verlag, 1977.40-60.
[5] 崔景安. 时滞Lotka-Volterra系统的持久性及周期解 [J]. 数学学报, 2004(5):511-520.doi:10.3321/j.issn:0583-1431.2004.03.013.

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备注/Memo

备注/Memo:
福建省自然科学基金资助项目(Z0511026)
更新日期/Last Update: 2014-03-23