Dynamics and pattern formation in a diffusive predator-prey system with strong Allee effect in prey

被引：209

作者：

Wang, Jinfeng ^{[2
,3
,4
]}

Shi, Junping ^{[1
]}

Wei, Junjie ^{[4
]}

机构：

[1] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

[2] Harbin Normal Univ, Sch Math, Harbin 150025, Heilongjiang, Peoples R China

[3] Harbin Normal Univ, YY Tseng Funct Anal Res Ctr, Harbin 150025, Heilongjiang, Peoples R China

[4] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 251卷 / 4-5期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

Reaction-diffusion system; Predator-prey; Bifurcation; Strong Allee effect; Spatiotemporal patterns; SPATIOTEMPORAL COMPLEXITY; GLOBAL BIFURCATION; PATCHY INVASION; MODEL; SEMIFLOWS; EXISTENCE; BEHAVIOR; CHAOS;

D O I：

10.1016/j.jde.2011.03.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The dynamics of a reaction-diffusion predator-prey system with strong Allee effect in the prey population is considered. Nonexistence of nonconstant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as nonconstant steady state solutions are studied. These results show that the impact of the Allee effect essentially increases the system spatiotemporal complexity. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1276 / 1304

页数：29

共 60 条

[1] APPLICATION OF THE INVARIANCE PRINCIPLE TO REACTION-DIFFUSION EQUATIONS [J].

ALIKAKOS, ND .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1979, 33 (02) :201-225

[2]

[Anonymous], 1994, GRUNDLEHREN MATH WIS

[3]

[Anonymous], 2003, WILEY SERIES MATH CO

[4]

[Anonymous], 1931, Animal aggregation: a study in general sociology

[5]

[Anonymous], 1982, Modelling fluctuating populations

[6]

[Anonymous], 1995, J DYN DIFFER EQU, DOI DOI 10.1007/BF02218815

[7] How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses [J].

Boukal, David S. ;

Sabelis, Maurice W. ;

Berec, Ludek .

THEORETICAL POPULATION BIOLOGY, 2007, 72 (01) :136-147

[8] PERMANENCE IN ECOLOGICAL-SYSTEMS WITH SPATIAL HETEROGENEITY [J].

CANTRELL, RS ;

COSNER, C ;

HUTSON, V .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1993, 123 :533-559

[9]

Chafee N., 1974, Applicable Analysis, V4, P17, DOI 10.1080/00036817408839081

[10] LARGE TIME BEHAVIOR OF SOLUTIONS OF SYSTEMS OF NON-LINEAR REACTION-DIFFUSION EQUATIONS [J].

CONWAY, E ;

HOFF, D ;

SMOLLER, J .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1978, 35 (01) :1-16

← 1 2 3 4 5 6 →