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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Bifurcation Analysis of a Discretized Prey-Predator System with Harvesting Effect on the Predator

Discontinuity, Nonlinearity, and Complexity 13(2) (2024) 229--246 | DOI:10.5890/DNC.2024.06.002

Karima Mokni, Rachid Fakhar, Mohamed Ch-Chaoui

Facult'{e} Polydisciplinaire Khouribga, Sultan My Slimane University, Khouribga, Morocco

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Abstract

We study the dynamic behavior of a discretized prey-predator system in this research. The model is formulated in terms of difference equations and derived by using the piecewise method, which takes into consideration the non-overlapping generations.  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 period-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 is stabilized using two different chaos control methods. Lastly, we verify our theoretical findings and provide more complex dynamics through computer analysis and numerical simulations.

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