In addition, some numerical simulations are given to verify the theoretical results obtained.
📌 3 Key Takeaways
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Objective & Hypothesis:This article is about the dynamic behavior of a prey-predator model exposed to the harvesting effect on prey.
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Key Findings & Data:The hybrid control strategy is applied to control the chaos caused by the Neimark-Sacker bifurcation.
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Conclusion & Impact:In addition, some numerical simulations are given to verify the theoretical results obtained.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Prey-Predator Model · Fixed point · Stability
Abstract
This article is about the dynamic behavior of a prey-predator model exposed to the harvesting effect on prey. Firstly, the existence and stability of the fixed points of the model are obtained, and then the presence and direction of Neimark-Sacker bifurcation is examined. By using the bifurcation theory, we show that the system undergoes Neimark-Sacker bifurcation. The hybrid control strategy is applied to control the chaos caused by the Neimark-Sacker bifurcation. In addition, some numerical simulations are given to verify the theoretical results obtained.
GÜMÜŞ, Ö. A. (2022). Dynamics of a Prey-Predator System with Harvesting Effect on Prey. Chaos Theory and Applications, Cilt: 4 - Sayı: 3, 144–151. https://ajindex.com/articles/858325
Clark, CW., 1985 Bioeconomic modelling and fisheries management. Wiley: New York. Clark CW., 1990 Mathematical bioeconomics: The optimal management of renewable resource. 2nd edition. John Wiley and Sons: New York. Danca, M.F., M. Feckan, N. Kuznetsov and G. Chen, 2019 Rich dynamics and anticontrol of extinction in a prey–predator system. Nonlinear Dynamics 98:1421–1445.
Din Q., Ö.A. Gümüş, H. Khalil, 2017 Neimark–Sacker bifurcation and chaotic behaviour of a modified Host–Parasitoid model. Zeitschrift für Naturforschung A. 72: 25–37. Elaydi S.N., 1996 An Introduction to Difference Equations Springer-Verlag, New York, NY, USA. Elsadany, A.A., H.A. El-Metwally, E. M. Elabbasy and H.N. Agiza, 2012 Chaos and bifurcation of a nonlinear discrete prey–predator system. Computational Ecology and Software 2: 169–180. Gümüş Ö.A., 2015 Dynamical consequences and stability analysis of a new host-parasitoid model, General Mathematics Notes 27: 9-16.
Gümüş, Ö.A., 2014 Global and local stability analysis in a nonlinear discrete time population model, Advances in Difference Equations 299: 1687–1847. Gümüş Ö.A., 2020 Neimark-Sacker bifurcation and stability a prey-predator system. Miskolc Mathematical Notes 21: 873-875. [Gümüş Ö.A., Q. Cui, A.G.M Selvam and A. Vianny, 2022 Global stability and bifurcation analysis of a discrete time SIR epidemic model. Miskolc Mathematical Notes 23: 193-210.
Gümüş, Ö.A. and M. Feckan, 2021
Stability, Neimark-Sacker bifurcation and chaos control for a prey-predator system with harvesting effect on predator. Miskolc Mathematical Notes 22: 663-679.
Gümüş, Ö.A. and F. Kangalgil, 2015 Allee effect and stability in a discrete-time host-parasitoid model. Journal of Advanced research in Applied Mathematics 7: 94-99. Gümüş Ö.A. and H. Köse, 2012 Allee effect on a new delay population model and stability analysis. Journal of Pure and Applied Mathematics: Advances and Applications, 7: 21-31.
Gümüş, Ö.A., A.G.M. Selvam R. and Dhineshbabu, 2022 Bifurcation analysis and chaos control of the population model with harvest. International Journal of Nonlinear Analysis and Applications 13: 115-125.
Gümüş, Ö.A., A.G.M. Selvam and R. Janagaraj, 2020 Stability of Modified Host-Parasitoid Model with Allee Effect, Applications and Applied Mathematics: An International Journal 15: 1032-1045.
Gümüş, Ö.A., A.G.M. Selvam and D. A. Vianny, 2019 Bifurcation and stability analysis of a discrete time SIR epidemic model with vaccination, International Journal of Analysis