Chaos Control, Codimension-One and Codimension-Two 1 : 2 Strong Resonance Bifurcation Analysis of a Predator-Prey Model with Holling Types I and III Functional Responses
We study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension-one and codimension-two bifurcation analysis, and chaos control in a predator-prey model with Holling types I and III functional responses. It is proven that the model has a trivial equili...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2024/5782500 |
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| author | Abdul Qadeer Khan Syeda Noor-ul-Huda Naqvi Shaimaa A. A. Ahmed Waleed A. I. El-Morsi |
| author_facet | Abdul Qadeer Khan Syeda Noor-ul-Huda Naqvi Shaimaa A. A. Ahmed Waleed A. I. El-Morsi |
| author_sort | Abdul Qadeer Khan |
| collection | DOAJ |
| description | We study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension-one and codimension-two bifurcation analysis, and chaos control in a predator-prey model with Holling types I and III functional responses. It is proven that the model has a trivial equilibrium point for all involved parameters but interior and semitrivial equilibrium solutions under certain model parameter conditions. Furthermore, local stability at trivial, semitrivial, and interior equilibria using the theory of linear stability is investigated. We have also explored the bifurcation sets for trivial, semitrivial, and interior equilibria and proved that flip bifurcation occurs at semitrivial equilibrium. Furthermore, it is also proven that Neimark–Sacker bifurcation as well as flip bifurcation occurs at an interior equilibrium solution, and in addition, at the same equilibrium solution, we also studied codimension-two 1:2 strong resonance bifurcation. Then, OGY and hybrid control strategies are employed to manage chaos in the model under study, which arises from Neimark–Sacker and flip bifurcations, respectively. We have also examined the preservation of the positive solution of the understudied model. Finally, numerical simulations are given to verify the theoretical results. |
| format | Article |
| id | doaj-art-da7dee1418da459099bb8e2fd7a2ca9b |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-da7dee1418da459099bb8e2fd7a2ca9b2025-02-03T10:48:36ZengWileyComplexity1099-05262024-01-01202410.1155/2024/5782500Chaos Control, Codimension-One and Codimension-Two 1 : 2 Strong Resonance Bifurcation Analysis of a Predator-Prey Model with Holling Types I and III Functional ResponsesAbdul Qadeer Khan0Syeda Noor-ul-Huda Naqvi1Shaimaa A. A. Ahmed2Waleed A. I. El-Morsi3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsWe study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension-one and codimension-two bifurcation analysis, and chaos control in a predator-prey model with Holling types I and III functional responses. It is proven that the model has a trivial equilibrium point for all involved parameters but interior and semitrivial equilibrium solutions under certain model parameter conditions. Furthermore, local stability at trivial, semitrivial, and interior equilibria using the theory of linear stability is investigated. We have also explored the bifurcation sets for trivial, semitrivial, and interior equilibria and proved that flip bifurcation occurs at semitrivial equilibrium. Furthermore, it is also proven that Neimark–Sacker bifurcation as well as flip bifurcation occurs at an interior equilibrium solution, and in addition, at the same equilibrium solution, we also studied codimension-two 1:2 strong resonance bifurcation. Then, OGY and hybrid control strategies are employed to manage chaos in the model under study, which arises from Neimark–Sacker and flip bifurcations, respectively. We have also examined the preservation of the positive solution of the understudied model. Finally, numerical simulations are given to verify the theoretical results.http://dx.doi.org/10.1155/2024/5782500 |
| spellingShingle | Abdul Qadeer Khan Syeda Noor-ul-Huda Naqvi Shaimaa A. A. Ahmed Waleed A. I. El-Morsi Chaos Control, Codimension-One and Codimension-Two 1 : 2 Strong Resonance Bifurcation Analysis of a Predator-Prey Model with Holling Types I and III Functional Responses Complexity |
| title | Chaos Control, Codimension-One and Codimension-Two 1 : 2 Strong Resonance Bifurcation Analysis of a Predator-Prey Model with Holling Types I and III Functional Responses |
| title_full | Chaos Control, Codimension-One and Codimension-Two 1 : 2 Strong Resonance Bifurcation Analysis of a Predator-Prey Model with Holling Types I and III Functional Responses |
| title_fullStr | Chaos Control, Codimension-One and Codimension-Two 1 : 2 Strong Resonance Bifurcation Analysis of a Predator-Prey Model with Holling Types I and III Functional Responses |
| title_full_unstemmed | Chaos Control, Codimension-One and Codimension-Two 1 : 2 Strong Resonance Bifurcation Analysis of a Predator-Prey Model with Holling Types I and III Functional Responses |
| title_short | Chaos Control, Codimension-One and Codimension-Two 1 : 2 Strong Resonance Bifurcation Analysis of a Predator-Prey Model with Holling Types I and III Functional Responses |
| title_sort | chaos control codimension one and codimension two 1 2 strong resonance bifurcation analysis of a predator prey model with holling types i and iii functional responses |
| url | http://dx.doi.org/10.1155/2024/5782500 |
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