Hopf bifurcation for a delayed predatorprey diffusion system with Dirichlet boundary condition

doi:10.1016/j.amc.2017.05.012

	Hopf bifurcation for a delayed predatorprey diffusion system with Dirichlet boundary condition
	Ma, Zhan-Ping 1; Huo, Hai-Feng 2; Xiang, Hong 2
刊名	Applied Mathematics and Computation
	2017-10-15
卷号	311 页码:1-18
关键词	Boundary conditions Diffusion Feedback Predator prey systems Time delay Bifurcation parameter Direction of hopf bifurcations Dirichlet boundary condition Existence and stability Feedback time delays Implicit function theorem Positive steady state Steady state solution
ISSN号	00963003
DOI	10.1016/j.amc.2017.05.012
英文摘要	A delayed predatorprey diffusion system with BeddingtonDeAngelis 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 τ 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. © 2017 Elsevier Inc.
语种	英语
出版者	Elsevier Inc.
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/114550]
专题	学科建设与学位办公室理学院
作者单位	1.School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo; Henan; 454003, China; 2.Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou; Gansu; 730050, China
推荐引用方式 GB/T 7714	Ma, Zhan-Ping,Huo, Hai-Feng,Xiang, Hong. Hopf bifurcation for a delayed predatorprey 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 predatorprey diffusion system with Dirichlet boundary condition.Applied Mathematics and Computation,311,1-18.
MLA	Ma, Zhan-Ping,et al."Hopf bifurcation for a delayed predatorprey diffusion system with Dirichlet boundary condition".Applied Mathematics and Computation 311(2017):1-18.