Codimension-two bifurcation analysis of a discrete predator–prey system with fear effect and Allee effect

In this paper, we study the dynamic behavior of a discrete predator–prey model with fear effect and Allee effect by theoretical analysis and numerical simulation. Firstly, the existence and stability of the equilibrium points of the model are proved. Secondly, the existence of codimension-2 bifurca...

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Main Authors: Ceyu Lei, Xiaoling Han
Format: Article
Language:English
Published: Vilnius University Press 2025-03-01
Series:Nonlinear Analysis
Subjects:
Online Access:https://www.journals.vu.lt/nonlinear-analysis/article/view/38977
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author Ceyu Lei
Xiaoling Han
author_facet Ceyu Lei
Xiaoling Han
author_sort Ceyu Lei
collection DOAJ
description In this paper, we study the dynamic behavior of a discrete predator–prey model with fear effect and Allee effect by theoretical analysis and numerical simulation. Firstly, the existence and stability of the equilibrium points of the model are proved. Secondly, the existence of codimension-2 bifurcations (1 : 2, 1 : 3, and 1 : 4 strong resonances) in the case of two parameters is verified by bifurcation theory. In order to illustrate the complexity of the dynamic behavior of the model in the two-parameter space, we simulate the bifurcation diagrams, phase diagrams, maximum Lyapunov exponent diagrams, and isoperiodic diagram, and we verify the influence of model parameters on the population size.
format Article
id doaj-art-22a5e4d41d4f4afb94adf08371136caf
institution Kabale University
issn 1392-5113
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language English
publishDate 2025-03-01
publisher Vilnius University Press
record_format Article
series Nonlinear Analysis
spelling doaj-art-22a5e4d41d4f4afb94adf08371136caf2025-08-20T03:54:48ZengVilnius University PressNonlinear Analysis1392-51132335-89632025-03-013010.15388/namc.2025.30.38977Codimension-two bifurcation analysis of a discrete predator–prey system with fear effect and Allee effectCeyu Lei0https://orcid.org/0000-0002-3742-6844Xiaoling Han1Northwest Normal UniversityNorthwest Normal University In this paper, we study the dynamic behavior of a discrete predator–prey model with fear effect and Allee effect by theoretical analysis and numerical simulation. Firstly, the existence and stability of the equilibrium points of the model are proved. Secondly, the existence of codimension-2 bifurcations (1 : 2, 1 : 3, and 1 : 4 strong resonances) in the case of two parameters is verified by bifurcation theory. In order to illustrate the complexity of the dynamic behavior of the model in the two-parameter space, we simulate the bifurcation diagrams, phase diagrams, maximum Lyapunov exponent diagrams, and isoperiodic diagram, and we verify the influence of model parameters on the population size. https://www.journals.vu.lt/nonlinear-analysis/article/view/38977discrete modelstabilitycodimension-2 bifurcationchaos
spellingShingle Ceyu Lei
Xiaoling Han
Codimension-two bifurcation analysis of a discrete predator–prey system with fear effect and Allee effect
Nonlinear Analysis
discrete model
stability
codimension-2 bifurcation
chaos
title Codimension-two bifurcation analysis of a discrete predator–prey system with fear effect and Allee effect
title_full Codimension-two bifurcation analysis of a discrete predator–prey system with fear effect and Allee effect
title_fullStr Codimension-two bifurcation analysis of a discrete predator–prey system with fear effect and Allee effect
title_full_unstemmed Codimension-two bifurcation analysis of a discrete predator–prey system with fear effect and Allee effect
title_short Codimension-two bifurcation analysis of a discrete predator–prey system with fear effect and Allee effect
title_sort codimension two bifurcation analysis of a discrete predator prey system with fear effect and allee effect
topic discrete model
stability
codimension-2 bifurcation
chaos
url https://www.journals.vu.lt/nonlinear-analysis/article/view/38977
work_keys_str_mv AT ceyulei codimensiontwobifurcationanalysisofadiscretepredatorpreysystemwithfeareffectandalleeeffect
AT xiaolinghan codimensiontwobifurcationanalysisofadiscretepredatorpreysystemwithfeareffectandalleeeffect