具有混合时滞的脉冲合作系统正周期解的存在性
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摘要
本文首先建立了具有变时滞和分布时滞的Lotka-Volterra两种群脉冲合作系统.然后通过应用Gaines和Mawhin叠合度定理,研究得到了具有变时滞和分布时滞的Lotka-Volterra两种群脉冲合作系统正周期解存在性的充分条件.
First, we established a class of non-autonomous two species impulsive Lotka-Volterra cooperative system with variable time delays and distributed time delays, then via employing the coincidence degree theory developed by Gaines and Mawhin to established sufficient conditions for the existence of positive periodic solutions of the system.
First, we established a class of non-autonomous two species impulsive Lotka-Volterra cooperative system with variable time delays and distributed time delays, then via employing the coincidence degree theory developed by Gaines and Mawhin to established sufficient conditions for the existence of positive periodic solutions of the system.
引文
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[9]Gaines R E,Mawhin J L.Coincidence degree and nonlinear differential equations[M].Berlin:Springer,1977.
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[2]Zhang Z,Wu J,Wang Z.Periodic solutions of nonautonomous stage-structured cooperative system[J].Comput Math Appl,2004,47:699-706.
[3]Yan J.Global positive periodic solutions of periodic n-species competition systems[J].Math Anal Appl,2009,356:288-294.
[4]Zhao H,Ding N.Existence and global attractivity of positive periodic solution for competition-predator system with variable delays[J].Chaos Solitons and Fractals,2006,29:162-170.
[5]Lu S.On the existence of positive periodic solutions to a Lotka-Volterra cooperative population model with multiple delays[J].Nonl Anal:Theo Meth Appl,2008,68(6):1746-1753.
[6]Chen F.Positive periodic solutions of neutral Lotka-Volterra system with feedback control[J].Appl Math Comput,2005,162:1279-1302.
[7]Wang X,Wang W,Lin X.Dynamics of a periodic Watt-type predator-prey system with impulsive effect[J].Chaos,Solitons and Fractals,2009,39(3):1270-1282.
[8]谭德君.具有生育脉冲的Lotka-Volterra合作系统的正周期解的存在性[J].生物数学学报,2004,19(4):414-420.
[9]Gaines R E,Mawhin J L.Coincidence degree and nonlinear differential equations[M].Berlin:Springer,1977.
[10]张恭庆,林源渠.泛函分析讲义[M].北京:北京大学出版社,1987.