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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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
Online AccessGet full text
ISSN1076-2787
1099-0526
1099-0526
DOI10.1155/2022/5715922

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Abstract 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.
AbstractList 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.
Audience Academic
Author Guo, Yanfeng
Ke, Changcheng
Yi, Ming
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CitedBy_id crossref_primary_10_1142_S0218127424500822
crossref_primary_10_3934_math_2024063
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ContentType Journal Article
Copyright Copyright © 2022 Changcheng Ke et al.
COPYRIGHT 2022 John Wiley & Sons, Inc.
Copyright © 2022 Changcheng Ke et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0
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Snippet 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...
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...
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SubjectTerms 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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Title Qualitative Analysis of a Spatiotemporal Prey-Predator Model with Additive Allee Effect and Fear Effect
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