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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| Language: | English |
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Vilnius University Press
2025-03-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://www.journals.vu.lt/nonlinear-analysis/article/view/38977 |
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| _version_ | 1849307280705585152 |
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| author | Ceyu Lei Xiaoling Han |
| author_facet | Ceyu Lei Xiaoling Han |
| author_sort | Ceyu Lei |
| collection | DOAJ |
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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.
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| format | Article |
| id | doaj-art-22a5e4d41d4f4afb94adf08371136caf |
| institution | Kabale University |
| issn | 1392-5113 2335-8963 |
| 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 |