Dynamics of a predator–prey model with nonlinear growth rate and B–D functional response

In this paper, a predator–prey diffusive model, subject to homogeneous Dirichlet boundary conditions, with Beddington–DeAngelis functional response and nonlinear growth rate on the predator is proposed and the well posedness of its solution is systematically studied. Taking the capture rate m as the...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 70; p. 103766
Main Authors Feng, Xiaozhou, Sun, Cong, Yang, Wenbin, Li, Changtong
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2023
Subjects
Existence
Numerical simulations
Positive solutions
Predator–prey diffusive model
Stability
Numerical simulations
Stability
Positive solutions
Predator–prey diffusive model
Existence
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Summary:In this paper, a predator–prey diffusive model, subject to homogeneous Dirichlet boundary conditions, with Beddington–DeAngelis functional response and nonlinear growth rate on the predator is proposed and the well posedness of its solution is systematically studied. Taking the capture rate m as the main parameter, we mainly investigate the existence, stability and exact number of positive solutions when m is large and other parameters meet a certain range of conditions. Meanwhile, some numerical simulations are applied to illustrate the analytical results. The main techniques used in this paper include the fixed point index theory, the super-sub solution method, the Lyapunov-Schmidt reduction procedure and the perturbation principle.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2022.103766