Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system

被引：448
|
作者：
Yi, Fengqi [2 ]
Wei, Junjie [2 ]
Shi, Junping [1 ,3 ]
机构：
[1] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA
[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
[3] Harbin Normal Univ, Sch Math, Harbin 150025, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 246卷 / 05期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
Diffusive predator-prey system; Holling type-II functional response; Hopf bifurcation; Steady state bifurcation; Spatially non-homogeneous periodic orbits; Global bifurcation; LYAPUNOV FUNCTIONS; POSITIVE SOLUTIONS; HOPF-BIFURCATION; LIMIT-CYCLES; MODEL; BEHAVIOR; STABILITY;
D O I：
10.1016/j.jde.2008.10.024
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A diffusive predator-prey system with Holling type-II predator functional response subject to Neumann boundary conditions is considered. Hopf and steady state bifurcation analysis are carried out in details. In particular we show the existence of multiple spatially non-homogeneous periodic orbits while the system parameters are all spatially homogeneous. Our results and global bifurcation theory also suggest the existence of loops of spatially non-homogeneous periodic orbits and steady state solutions. These results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulation. (c) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码：1944 / 1977
页数：34
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