一类捕食-食饵反应扩散系统的行波解
|
摘要
文章讨论了一类带有Beddington-DeAngelis型功能反应函数、捕获项及阶段性结构的捕食-食饵反应扩散系统。通过构造上下解,利用Schauder不动点定理证明了该系统行波解的存在性。
The paper is concerned with a predator-prey reaction-diffusion system equipped with Beddington-DeAngelis functional response,harvesting and stage structure.By constructing apair of upper-lower solutions and employing the Schauder's fixed point theorem,we obtain the existence of traveling wave of the system.
The paper is concerned with a predator-prey reaction-diffusion system equipped with Beddington-DeAngelis functional response,harvesting and stage structure.By constructing apair of upper-lower solutions and employing the Schauder's fixed point theorem,we obtain the existence of traveling wave of the system.
引文
[1] Liu M,Wang K.Global Stability of Stage-structured Predator-prey Models with Beddington-DeAngelis Functional Response[J].Commun Nonlinear Sci Numer Simulat,2011,16:3792-3797.DOI:10.1016/j.cnsns.2010.12.026.
[2] Shi X,Zhou X,Song X Y.Analisis of a Stage-structured Predator-prey Model with Crowley-Martin Function[J].J Appl Math Comput,2011,36:459-472.DOI:10.1007/s12190-010-0413-8.
[3] Liu W,Jiang Y.Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting[J].East Asian Journal on Applied Mathematics,2017,7:376-395.DOI:10.4208/eajam.020916.250217a.
[4]彭华勤,朱庆,肖华锋.具有时滞离散时间捕食-食饵模型的行波解[J].郑州大学学报(理学版),2017,49:37-42.DOI:10.13705/j.issn.1671-6841.2016219.
[5] Song X Y,Chen L S.Optimal Harvesting and Stability for a Predator-prey System with Stage Structure[J].Acta Math Appl Sin,2002,18:307-314.DOI:https:∥doi.org/10.1007/s102550200.
[6]叶其孝.反应扩散方程引论[M].北京:科学出版社,2011.
[7] Hong K,Weng P X.Stability and Traveling Waves of a Stage-structured Predator-prey Model with Holling-ll Functional Response and Harvesting[J].Nonlinear Anal Real World Appl,2013,14:83-103.DOI:10.1016/j.nonrwa.2012.05.004.
[8] Huang J,Zou X.Traveling Wavefronts in Diffusive and Cooperative Lotka-Volterra System with Delay[J].J Math Anal Appl,2002,271:455-466.DOI:https:∥doi.org/10.1016/S0022-247X(02)00135-X.
[9] Lv Y F,Yuan R,Pei Y Z.Effect of Harvesting,Delay and Diffusion in a Generalist Predator-prey Model[J].Appl Math Comput,2014,226:348-366.DOI:https:∥doi.org/10.1016/j.amc.2013.10.071.
[10] Skalaski G T,Gilliam J F.Functional Responses with Predator Interference:Viable Alternatives to the Holling Tuye ll Model[J].Ecology,2001,82:3083-3092.DOI:10.1890/0012-9658(2011)082[3083:FRWPIV]2.0.CO;2.
[2] Shi X,Zhou X,Song X Y.Analisis of a Stage-structured Predator-prey Model with Crowley-Martin Function[J].J Appl Math Comput,2011,36:459-472.DOI:10.1007/s12190-010-0413-8.
[3] Liu W,Jiang Y.Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting[J].East Asian Journal on Applied Mathematics,2017,7:376-395.DOI:10.4208/eajam.020916.250217a.
[4]彭华勤,朱庆,肖华锋.具有时滞离散时间捕食-食饵模型的行波解[J].郑州大学学报(理学版),2017,49:37-42.DOI:10.13705/j.issn.1671-6841.2016219.
[5] Song X Y,Chen L S.Optimal Harvesting and Stability for a Predator-prey System with Stage Structure[J].Acta Math Appl Sin,2002,18:307-314.DOI:https:∥doi.org/10.1007/s102550200.
[6]叶其孝.反应扩散方程引论[M].北京:科学出版社,2011.
[7] Hong K,Weng P X.Stability and Traveling Waves of a Stage-structured Predator-prey Model with Holling-ll Functional Response and Harvesting[J].Nonlinear Anal Real World Appl,2013,14:83-103.DOI:10.1016/j.nonrwa.2012.05.004.
[8] Huang J,Zou X.Traveling Wavefronts in Diffusive and Cooperative Lotka-Volterra System with Delay[J].J Math Anal Appl,2002,271:455-466.DOI:https:∥doi.org/10.1016/S0022-247X(02)00135-X.
[9] Lv Y F,Yuan R,Pei Y Z.Effect of Harvesting,Delay and Diffusion in a Generalist Predator-prey Model[J].Appl Math Comput,2014,226:348-366.DOI:https:∥doi.org/10.1016/j.amc.2013.10.071.
[10] Skalaski G T,Gilliam J F.Functional Responses with Predator Interference:Viable Alternatives to the Holling Tuye ll Model[J].Ecology,2001,82:3083-3092.DOI:10.1890/0012-9658(2011)082[3083:FRWPIV]2.0.CO;2.