Qualitative Analysis of a Spatiotemporal Prey-Predator Model with Additive Allee Effect and Fear Effect

A diffusive predator-prey system with both the additive Allee effect and the fear effect in the prey subject to Neumann boundary conditions is considered in this paper. Firstly, non-negative and non-trivial solution a priori estimations are shown. Furthermore, for specific parameter ranges, the abse...

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Bibliographic Details
Published inComplexity (New York, N.Y.) Vol. 2022; no. 1
Main Authors Ke, Changcheng, Yi, Ming, Guo, Yanfeng
Format Journal Article
LanguageEnglish
Published Hoboken Hindawi 2022
John Wiley & Sons, Inc
Wiley
Subjects
Analysis
Bifurcation theory
Boundary conditions
Eigenvalues
Equilibrium
Fear
Investigations
Mathematical models
Numerical analysis
Parameters
Predator-prey simulation
Predators
Qualitative analysis
Simulation methods
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Summary:A diffusive predator-prey system with both the additive Allee effect and the fear effect in the prey subject to Neumann boundary conditions is considered in this paper. Firstly, non-negative and non-trivial solution a priori estimations are shown. Furthermore, for specific parameter ranges, the absence of non-constant positive solutions is demonstrated. Secondly, we use the linearized theory to investigate the stability of non-negative constant solutions. The spatially homogeneous and non-homogeneous periodic solutions, as well as non-constant steady state solutions, are next investigated by using Allee effect parameters as the bifurcation parameter. Finally, numerical simulation is used to illustrate some theoretical results.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1076-2787
1099-0526
DOI:10.1155/2022/5715922