具有时滞的两种群捕食者——食饵扩散系统的正周期解的存在性
Existence of Positive Periodic Solution for a Delayed Predator-prey Model of Prey Dispersal in Two-patch Environments
摘要
本文研究了一类具有时滞的Lotka-Volterra类型的两种群捕食者——食饵扩散系统,利用Mawhin的重合度理论建立了这类系统的正周期解存在的一个充分条件。
A delayed periodic Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments is investigated.A sufficient condition of the existence of positive periodic solution is established for the system by using Gaines and Mawhin＇s continuation theorem of coincidence degree theory.
出处
《安庆师范学院学报（自然科学版）》
2006年第2期15-20,共6页
Journal of Anqing Teachers College(Natural Science Edition)
关键词
捕食者——食饵扩散系统
正周期解
重合度理论
predator-prey diffusive system, positive periodic solution, coincidence degree theory
参考文献14
-
1R.E.Gaines,J.L.Mawhin,Coincidence Degree and Nonlinear Differential Equation[M].Spring Berlin,1977.
-
2Goh B.S.Global stability in two species interactions[J].J.Math.Biol.,1976,313-318.
-
3Hastings A.,Global stability in two species systems[J].J.Math.boil.,1978,399-403.
-
4He X.Z.,Stability and delays in a predator-prey system[J].J.Math.Appl.,1996,355-370.
-
5Cushing J.M.,Integro-differential equations and delay models in a population dynamics,in Lecture Notes in Bionmathematics[J].Berlin,Heidelberg:Springer-Verlag,1977,20.
-
6Kuang Y.Delay differential equations with applications in population dynamics[M].NewYork:AdemicPress,1983.
-
7Freedman H.I.,Bao V.S.H.The tradeoff between mutual interference and time lag in predator-preysystems[J].Bull.Math.Boil.,1983,991-1004.
-
8Freedman H.I.,So J.and Waltman P.Coexistence in a model of competition in the chemostat incorporating discrete time delays[J].SIAM J.Appl.Math.,1989,859-870.
-
9Kuang Y.,Beretta E.,Global qualitative analysis of a ratio-dependent predator-prey system[J].J.Math,Biol.,1998,36:389-406.
-
10Levin S.A.Dispersion and population interaction[J].The Amer.Naturalist.,1974,10:207-228.
