Hopf bifurcation for a delayed predator-prey diffusion system with Dirichlet boundary condition | |
Ma, Zhan-Ping1; Huo, Hai-Feng2; Xiang, Hong2 | |
刊名 | APPLIED MATHEMATICS AND COMPUTATION
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2017-10-15 | |
卷号 | 311页码:1-18 |
关键词 | Predator prey system Diffusion Time delay Steady-state solution Hopf bifurcation |
ISSN号 | 0096-3003 |
DOI | 10.1016/j.amc.2017.05.012 |
英文摘要 | A delayed predator prey diffusion system with Beddington-DeAngelis functional response under Dirichlet boundary condition is investigated. The existence and stability of the positive spatially nonhomogeneous steady-state solution are obtained via the implicit function theorem. Moreover, taking feedback time delay tau as the bifurcation parameter, Hopf bifurcation near the positive steady-state solution is proved to occur at a sequence of critical values, we can show that feedback time delay can induce nonhomogeneous periodic oscillatory patterns. The direction of Hopf bifurcation is forward when parameter m in model (1.2) is sufficiently large. Numerical simulations and numerical solutions are presented to illustrate our theoretical results. (C) 2017 Elsevier Inc. All rights reserved. |
资助项目 | Institutions of higher learning scientific research project of Henan Province of China[15A110002] ; Fundamental Research Funds for the Universities of Henan Province of China[NSFRF140141] ; Doctor's Foundation of Henan Polytechnic University[B2014-059] ; National Natural Science Foundation of China[11461041][11661050] ; NSF of Gansu Province[148RJZA024] |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | ELSEVIER SCIENCE INC |
WOS记录号 | WOS:000404324900001 |
状态 | 已发表 |
内容类型 | 期刊论文 |
源URL | [http://119.78.100.223/handle/2XXMBERH/33056] ![]() |
专题 | 理学院 材料科学与工程学院 学科建设与学位办公室 |
通讯作者 | Huo, Hai-Feng |
作者单位 | 1.Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454003, Henan, Peoples R China 2.Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Gansu, Peoples R China |
推荐引用方式 GB/T 7714 | Ma, Zhan-Ping,Huo, Hai-Feng,Xiang, Hong. Hopf bifurcation for a delayed predator-prey diffusion system with Dirichlet boundary condition[J]. APPLIED MATHEMATICS AND COMPUTATION,2017,311:1-18. |
APA | Ma, Zhan-Ping,Huo, Hai-Feng,&Xiang, Hong.(2017).Hopf bifurcation for a delayed predator-prey diffusion system with Dirichlet boundary condition.APPLIED MATHEMATICS AND COMPUTATION,311,1-18. |
MLA | Ma, Zhan-Ping,et al."Hopf bifurcation for a delayed predator-prey diffusion system with Dirichlet boundary condition".APPLIED MATHEMATICS AND COMPUTATION 311(2017):1-18. |
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