Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting
In this paper, we investigate the dynamical behavior of a two dimensional discretized prey predator system. The model is formulated in terms of difference equations and derived by using the higher-order implicit Runge Kutta method with a very small step size to attain a discrete time version of its...
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| Language: | English |
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Miskolc University Press
2024-01-01
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| Series: | Miskolc Mathematical Notes |
| Online Access: | http://mat76.mat.uni-miskolc.hu/mnotes/article/4219 |
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| author | Karima Mokni Mohamed Ch-Chaoui |
| author_facet | Karima Mokni Mohamed Ch-Chaoui |
| author_sort | Karima Mokni |
| collection | DOAJ |
| description | In this paper, we investigate the dynamical behavior of a two dimensional discretized prey predator system. The model is formulated in terms of difference equations and derived by using the higher-order implicit Runge Kutta method with a very small step size to attain a discrete time version of its continuous counterpart. The existence of fixed points as well as their local asymptotic stability are proved. Further, it is shown that the model experiences Neimark-Sacker bifurcation (NSB for short) and the periodic doubling bifurcation (PDB) in a small neighborhood of the coexistence fixed point under certain parametric conditions. This analysis utilizes bifurcation theory and the center manifold theorem. The chaos influenced by NSB is stabilized. Finally, we use numerical simulations and computer analysis to check our theories and show more complex behaviors. |
| format | Article |
| id | doaj-art-52b8ef06c02e4ddaaf24b4b901085fc7 |
| institution | Kabale University |
| issn | 1787-2405 1787-2413 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Miskolc University Press |
| record_format | Article |
| series | Miskolc Mathematical Notes |
| spelling | doaj-art-52b8ef06c02e4ddaaf24b4b901085fc72025-01-21T12:00:07ZengMiskolc University PressMiskolc Mathematical Notes1787-24051787-24132024-01-0125292110.18514/MMN.2024.4219Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvestingKarima MokniMohamed Ch-ChaouiIn this paper, we investigate the dynamical behavior of a two dimensional discretized prey predator system. The model is formulated in terms of difference equations and derived by using the higher-order implicit Runge Kutta method with a very small step size to attain a discrete time version of its continuous counterpart. The existence of fixed points as well as their local asymptotic stability are proved. Further, it is shown that the model experiences Neimark-Sacker bifurcation (NSB for short) and the periodic doubling bifurcation (PDB) in a small neighborhood of the coexistence fixed point under certain parametric conditions. This analysis utilizes bifurcation theory and the center manifold theorem. The chaos influenced by NSB is stabilized. Finally, we use numerical simulations and computer analysis to check our theories and show more complex behaviors.http://mat76.mat.uni-miskolc.hu/mnotes/article/4219 |
| spellingShingle | Karima Mokni Mohamed Ch-Chaoui Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting Miskolc Mathematical Notes |
| title | Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting |
| title_full | Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting |
| title_fullStr | Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting |
| title_full_unstemmed | Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting |
| title_short | Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting |
| title_sort | dynamic analysis and chaos control in a discrete predator prey model with holling type iv and nonlinear harvesting |
| url | http://mat76.mat.uni-miskolc.hu/mnotes/article/4219 |
| work_keys_str_mv | AT karimamokni dynamicanalysisandchaoscontrolinadiscretepredatorpreymodelwithhollingtypeivandnonlinearharvesting AT mohamedchchaoui dynamicanalysisandchaoscontrolinadiscretepredatorpreymodelwithhollingtypeivandnonlinearharvesting |