一类带有食饵避难捕食-竞争扩散模型的定性分析
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摘要
主要研究了一类带有食饵避难捕食-竞争反应扩散系统的动力学行为,应用特征方程理论和Laypunov函数方法研究了系统平衡点的稳定性,运用拓扑度方法给出了非常值正稳态解的存在性.
The qualitative properties of the predation-competition reaction diffusion system with the prey refuge are considered.The conditions for the local asymptotic stability of the unique positive constant solution of the system are given by the eigenvalue function.In addition,it is shown that a priori upper and lower bounds for positive steady states of the system are established.Finally,the method of topological degree has been used to derive a set of sufficient conditions for the existence of at least one strictly positive non-trivial solution.
The qualitative properties of the predation-competition reaction diffusion system with the prey refuge are considered.The conditions for the local asymptotic stability of the unique positive constant solution of the system are given by the eigenvalue function.In addition,it is shown that a priori upper and lower bounds for positive steady states of the system are established.Finally,the method of topological degree has been used to derive a set of sufficient conditions for the existence of at least one strictly positive non-trivial solution.
引文
[1]叶其孝,李正元,王明新,等.反应扩散方程引论[M].北京:科学出版社,2011:38-176.
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[7]KO W,RYU K.Qualitative analysis of a predator-prey model with Holling typeⅡ:functional response incorporating aprey refuge[J].J Differential Equations,2006,231:534-550.
[8]HENRY D.Geometric theory of semilinear parabolic equations[M].Berlin:Springer-Verlag,1993:8-137.
[2]PENG R,WANG M X.Positive steady states of the Holling-Tanner prey-predator model with diffusion[J].Proc Roy Soc Edinburgh Sect A,2005,135:149-164.
[3]PANG P Y,WANG M X.Non-constant positive steady-states of a predator-prey system with non-monotonic functional response and diffusion[J].Proc London Math Soc,2004,88(3):135-157.
[4]VANGE RICHARD R.Predation and resource partitioning in one predator-two prey modle communities[J].The American Naturalist,1978,112:797-813.
[5]LIN C S,NI W M,TAKAI I.Large amplitude stationary solutions to a chemotaxis systems[J].J Differential Equations,1988,72:1-27.
[6]LOU Y,NI W M.Diffusion self-diffusion and cross-diffusion[J].J Differential Equations,1996,131:79-131.
[7]KO W,RYU K.Qualitative analysis of a predator-prey model with Holling typeⅡ:functional response incorporating aprey refuge[J].J Differential Equations,2006,231:534-550.
[8]HENRY D.Geometric theory of semilinear parabolic equations[M].Berlin:Springer-Verlag,1993:8-137.