On certain new exact solutions of a diffusive predator-prey system

被引：23

作者：

Kraenkel, R. A. ^{[2
]}

Manikandan, K. ^{[1
]}

Senthilvelan, M. ^{[1
]}

机构：

[1] Bharathidasan Univ, Ctr Nonlinear Dynam, Sch Phys, Tiruchirappalli 620024, Tamil Nadu, India

[2] Univ Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, Brazil

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2013年 / 18卷 / 05期

关键词：

Reaction-diffusion equations; Predator-prey system; (G '/G)-Expansion method; (G'/G)-EXPANSION METHOD;

D O I：

10.1016/j.cnsns.2012.09.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the (G'/G) expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：1269 / 1274

页数：6

共 16 条

[1]

Allee WC, 1938, SOCIAL LIFE OF ANIMA

[2] Application of the (G′/G)-expansion method for nonlinear evolution equations [J].

Bekir, Ahmet .

PHYSICS LETTERS A, 2008, 372 (19) :3400-3406

[3]

Courchamp F, 2008, ALLEE EFFECTS IN ECOLOGY AND CONSERVATION, P1

[4] New exact solutions of the (3+1)-dimensional Burgers system [J].

Dai, Chao-Qing ;

Wang, Yue-Yue .

PHYSICS LETTERS A, 2009, 373 (02) :181-187

[5]

DUBOIS D M, 1975, Ecological Modelling, V1, P67, DOI 10.1016/0304-3800(75)90006-X

[6] Symmetry analysis of an integrable reaction-diffusion equation [J].

Kraenkel, RA ;

Senthilvelan, M .

CHAOS SOLITONS & FRACTALS, 2001, 12 (03) :463-474

[7]

Murray JD., 2001, MATH BIOL

[8]

Okubo Akira., 2001, Diffusion_and_ecological_problems:_Modern_perspectives

[9] How predation can slow, stop or reverse a prey invasion [J].

Owen, MR ;

Lewis, MA .

BULLETIN OF MATHEMATICAL BIOLOGY, 2001, 63 (04) :655-684

[10] An exact solution of a diffusive predator-prey system [J].

Petrovskii, S ;

Malchow, H ;

Li, BL .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2005, 461 (2056) :1029-1053

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