一类具有B-D功能反应和Allee效应的非自治捕食系统的渐近性质
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摘要
建立了一类具有Beddington-DeAngelis功能反应和Allee效应的非自治捕食系统,充分利用微分不等式技巧等得到了系统一致持久生存的充分条件。对相应的周期系统,利用Browder不动点定理得到了系统周期解的存在性,同时通过构造一个特殊的Lyapunov函数得到了系统周期解全局渐近稳定的控制条件,最后用MATLAB软件对相关理论结果进行了数值模拟。
In this paper,a non-autonomous predator-prey system with Beddington-DeAngelis functional response and Allee effect was studied. Sufficient conditions for uniform persistence of the system were obtained by the skills of differential inequalities. For corresponding periodic system,globally asymptotic stability of the periodic solution was obtained by Browder's fixed point theory and constructing a suitable Lyapunov function. Finally,some numerical examples and simulations were given for the theoretical results by Matlab software.
In this paper,a non-autonomous predator-prey system with Beddington-DeAngelis functional response and Allee effect was studied. Sufficient conditions for uniform persistence of the system were obtained by the skills of differential inequalities. For corresponding periodic system,globally asymptotic stability of the periodic solution was obtained by Browder's fixed point theory and constructing a suitable Lyapunov function. Finally,some numerical examples and simulations were given for the theoretical results by Matlab software.
引文
[1]肖燕妮,周义仓,唐三一.生物数学原理[M].陕西西安:西安交通大学出版社,2012.
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[3]DEANGELIS D L,GOLDSTEIN R A,O'NEILL R V.Amodel for trophic interaction[J].Ecology,1975,56:881-892.
[4]FAN M,KUANG Y.Dynamics of a nonautonomous predator-prey system with beddington-DeAngelis functional response[J].Journal of Mathematical Analysis and Applications.2004,295:15-39.
[5]PALLAV J P,TAPAN S.Qualitative analysis of a predator-prey system with double allee effect in prey[J].Chaos,Solitons&Fractals,2015,73:36-63.
[6]BROWDER F E.The fixed point theory of multi-valued mappings in topological vector spaces[J].Mathematische Annalen,1968,177:183-301.
[7]BARBALAT I.Systems equations differential scillations nonlinears[J].Rev.Roumaine Math.Pures Appl.,1959,4(2):267-270.
[2]BEDDINGTON J R.Mutual interference between parasites or predators and its effect on searching efficiency[J].Journal of Animal Ecology,1975,44(1):331-340.
[3]DEANGELIS D L,GOLDSTEIN R A,O'NEILL R V.Amodel for trophic interaction[J].Ecology,1975,56:881-892.
[4]FAN M,KUANG Y.Dynamics of a nonautonomous predator-prey system with beddington-DeAngelis functional response[J].Journal of Mathematical Analysis and Applications.2004,295:15-39.
[5]PALLAV J P,TAPAN S.Qualitative analysis of a predator-prey system with double allee effect in prey[J].Chaos,Solitons&Fractals,2015,73:36-63.
[6]BROWDER F E.The fixed point theory of multi-valued mappings in topological vector spaces[J].Mathematische Annalen,1968,177:183-301.
[7]BARBALAT I.Systems equations differential scillations nonlinears[J].Rev.Roumaine Math.Pures Appl.,1959,4(2):267-270.