具有时滞离散时间捕食-食饵模型的行波解
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摘要
研究了一类抽象的离散时间时滞反应扩散系统,当非线性项满足部分指数拟单调条件时行波解的存在性.利用交叉迭代方法和Schauder不动点定理,将抽象波方程行波解的存在性转化为寻找一对合适的上下解,并将所得结论应用到具有时滞离散时间的捕食-食饵模型中.
The existence of traveling wave solutions for general discrete time reaction diffusive system with delay when the nonlinear term satisfies the partial exponential quasi monotone condition was investigated.By using the cross iteration method and Schauder's fixed point theorem,the existence of traveling wave solutions was reduced to search a pair of upper and lower solutions. Finally,a discrete time delay prey-predator type model with spatial diffusion was considered to illustrate the results.
The existence of traveling wave solutions for general discrete time reaction diffusive system with delay when the nonlinear term satisfies the partial exponential quasi monotone condition was investigated.By using the cross iteration method and Schauder's fixed point theorem,the existence of traveling wave solutions was reduced to search a pair of upper and lower solutions. Finally,a discrete time delay prey-predator type model with spatial diffusion was considered to illustrate the results.
引文
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[6]郝丽杰,蒋贵荣,鹿鹏.具有垂直传染的SIRS传染病模型分岔分析[J].郑州大学学报(理学版),2013,45(2):31-36.
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[2]HONG K,WENG P X.Stability and traveling waves of a stage-structured predator-prey model with holling type-II functional response and harvesting[J].Nonlinear Anal RWA,2013,14(1):83-103.
[3]ZHANG G B,LI W T,LIN G.Traveling waves in delayed predator-prey systems with nonlocal diffusion and stage structure[J].Mathematical and computer modelling,2009,49(5/6):1021-1029.
[4]ZHANG X,XU R.Global stability and travelling waves of a predator-prey model with diffusion and nonlocal maturation delay[J].Communications in nonlinear science and numerical simulation,2010,15(11):3390-3401.
[5]李秋英.具有时滞和不育控制的捕食模型的Hopf分支[J].郑州大学学报(理学版),2016,48(4):23-26.
[6]郝丽杰,蒋贵荣,鹿鹏.具有垂直传染的SIRS传染病模型分岔分析[J].郑州大学学报(理学版),2013,45(2):31-36.
[7]Roeger L I W.Dynamically consistent discrete Lotka-Volterra competition models derived from nonstandard finite-difference schemes[J].Discrete and continuous dynamical systems,2008,2(2):415-429.
[8]LIN G,LI W T.Traveling wave fronts in temporally discrete reaction-diffusion equations with delay[J].Nonlinear analysis real world applications,2008,9(1):197-205.
[9]XIA J,YU Z.Traveling wave solutions in temporally discrete reaction-diffusion systems with delays[J].Zamm-journal of applied mathematics and mechanics,2011,91(10):809-823.