Numerical simulation and qualitative analysis for a predator–prey model with B–D functional response

We consider a predator–prey model with Beddington–DeAngelis functional response subject to the homogeneous Neumann boundary condition. We study the local and global stability of the unique positive constant solution, the nonexistence of nonconstant positive solution. By bifurcation theorem we obtain...

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Bibliographic Details
Published inMathematics and computers in simulation Vol. 117; pp. 39 - 53
Main Authors Jiang, Hongling, Wang, Lijuan, Yao, Ruofei
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2015
Subjects
Beddington–DeAngelis
Existence
Numerical simulation
Predator–prey
Stability
Beddington–DeAngelis
Predator–prey
Numerical simulation
Stability
Existence
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Summary:We consider a predator–prey model with Beddington–DeAngelis functional response subject to the homogeneous Neumann boundary condition. We study the local and global stability of the unique positive constant solution, the nonexistence of nonconstant positive solution. By bifurcation theorem we obtain one sufficient condition of the existence of nonconstant positive steady state solution in one dimensional case. Furthermore, in numerical simulation, we design a path to analyze and complement our theoretical results.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2015.05.006