EXISTENCE OF TWO PERIODIC SOLUTIONS TO A RATIO-DEPENDENT PREDATOR-PREY MODEL WITH PREDATOR'S HARVEST

EXISTENCE OF TWO PERIODIC SOLUTIONS TO A RATIO-DEPENDENT PREDATOR-PREY MODEL WITH PREDATOR'S HARVEST

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摘要 In this paper, we study a non-autonomous ratio-dependent predator-prey model with predator＇s harvest. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least two positive periodic solutions of this model. In this paper, we study a non-autonomous ratio-dependent predator-prey model with predator＇s harvest. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least two positive periodic solutions of this model.

作者 Tian Desheng Wang Mei Zeng Xianwu

机构地区 College of Sciences College of Math. and Statistics

出处《Annals of Differential Equations》 2007年第4期492-498,共7页 微分方程年刊（英文版）

基金 the Scientific Research Foundation of the Doctor Department of Hubei University of Technology

关键词 predator-prey model RATIO-DEPENDENT predator＇s harvest periodic solution coincidence degree predator-prey model ratio-dependent predator＇s harvest periodic solution coincidence degree

分类号 O17 [理学—基础数学]

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参考文献1

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二级参考文献6

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共引文献22

1Qin Fajin,Deng Jin,Xu Daoyi.MULTIPLE PERIODICITY TO A CLASS OF DELAYED STATE-DEPENDENT PREDATOR-PREY SYSTEM[J].Annals of Differential Equations,2007,23(4):484-491.
2田德生.具有HollingIV类功能性反应时滞扩散捕食模型的多个周期解[J].数学的实践与认识,2007,37(24):107-114. 被引量：2
3TIAN Desheng,ZHANG Zhengqiu.Existence of Four Periodic Solutions of a Ratio-Dependent Predator-Prey Model with Exploited Terms[J].Wuhan University Journal of Natural Sciences,2008,13(1):1-5. 被引量：1
4田德生,李子强.具有时滞和反馈控制的非自治Schoner模型持续生存和周期解[J].工程数学学报,2008,25(2):343-352. 被引量：3
5田德生.一类时滞微分方程正周期解的存在性[J].数学的实践与认识,2008,38(11):163-167.
6Desheng TIAN.PERIODIC SOLUTION AND PERSISTENCE FOR A THREE-SPECIES RATIO-DEPENDENT PREDATOR-PREY MODEL WITH TIME DELAYS IN TWO-PATCH ENVIRONMENTS[J].Journal of Systems Science & Complexity,2008,21(2):226-238. 被引量：4
7TIAN De-sheng.Existence of two periodic solutions of a ratio-dependent Holling-Taner model with infinite delay and prey harvest[J].Applied Mathematics(A Journal of Chinese Universities),2008,23(2):136-142. 被引量：5
8田德生,朱长青,朱永松.Holling Ⅳ捕食-食饵时滞系统的多个周期解[J].纯粹数学与应用数学,2009,25(2):339-345. 被引量：6
9姚晓洁,秦发金.一类具有脉冲和非单调功能反应的捕食者-食饵系统的多重正周期解[J].数学的实践与认识,2009,39(17):227-234.
10周优军,秦发金,姚晓洁,曹亮.一类具有脉冲和非单调功能反应的扩散时滞捕食系统的多重正周期解[J].广西科学,2009,16(4):373-378.

1TIAN Desheng,ZHANG Zhengqiu.Existence of Four Periodic Solutions of a Ratio-Dependent Predator-Prey Model with Exploited Terms[J].Wuhan University Journal of Natural Sciences,2008,13(1):1-5. 被引量：1
2TIAN De-sheng.Existence of two periodic solutions of a ratio-dependent Holling-Taner model with infinite delay and prey harvest[J].Applied Mathematics(A Journal of Chinese Universities),2008,23(2):136-142. 被引量：5
3Bi Ping,Zhang Weipeng.MULTIPLE POSITIVE PERIODIC SOLUTIONS IN A IMPULSIVE PREDATOR-PREY SYSTEM WITH TYPEⅣFUNCTIONAL RESPONSES[J].Annals of Differential Equations,2007,23(4):391-399.
4郝心耀.“绿色重合性能量突变体系”新概念的提出及理论研究[J].绿色科技,2013,15(6):315-318.
5Qin Fajin,Deng Jin,Xu Daoyi.MULTIPLE PERIODICITY TO A CLASS OF DELAYED STATE-DEPENDENT PREDATOR-PREY SYSTEM[J].Annals of Differential Equations,2007,23(4):484-491.
6Xiao Hong LI,Chun LU,Xiu Feng DU.Permanence and Global Attractivity of a Discrete Semi-Ratio-Dependent Predator-Prey System with Holling Ⅳ Type Functional Response[J].Journal of Mathematical Research and Exposition,2010,30(3):442-450. 被引量：3
7LIJUAN ZHA,JING-AN CUI,XUEYONG ZHOU.RATIO-DEPENDENT PREDATOR-PREY MODEL WITH STAGE STRUCTURE AND TIME DELAY[J].International Journal of Biomathematics,2012,5(4):15-37. 被引量：2
8Huang Aimei(College of Math. and Computer Science,Fuzhou University,Fuzhou 350002).ON A NONAUTONOMOUS RATIO-DEPENDENT PREDATOR-PREY MODEL WITH TIME DELAY AND DIFFUSION[J].Annals of Differential Equations,2008,24(2):141-149.
9Jiandong Li(School of Mathematical Sciences,Luliang University,Luliang 033000,Shanxi).POSITIVE PERIODIC SOLUTIONS TO NEUTRAL RATIO-DEPENDENT PREDATOR-PREY SYSTEM[J].Annals of Differential Equations,2012,28(3):276-282.
10LIU Yan-wei,LIU Xia.Bifurcation and Limit Cycle of a Ratio-dependent Predator-prey, System with Refuge on Prey[J].Chinese Quarterly Journal of Mathematics,2013,28(2):234-240.

Annals of Differential Equations

2007年第4期

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EXISTENCE OF TWO PERIODIC SOLUTIONS TO A RATIO-DEPENDENT PREDATOR-PREY MODEL WITH PREDATOR'S HARVEST

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