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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

Dynamical Analysis and Chaos Control in a Discrete-Time Evolutionary Beverton-Holt Model

Discontinuity, Nonlinearity, and Complexity 12(4) (2023) 803--822 | DOI:10.5890/DNC.2023.12.007

Mohamed Ch-Chaoui, Karima Mokni

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

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Abstract

In this work, a discrete-time evolutionary Beverton-Holt population model is formulated. The existence and local asymptotic stability of the positive equilibrium point are studied. It is also shown that the discrete model can undergo a Neimark-Sacker bifurcation (NSB) in a small neighborhood of the positive equilibrium under certain conditions. In order to control chaos, we employ the Ott-Grebogi-Yorke (OGY) method and the hybrid control strategy to stabilize the unstable periodic orbits by using small perturbations applied to the derived system. Numerical simulations are developed with Matlab software, not only to verify our theoretical results but also to show more complex dynamics of the derived model, including invariant curves and chaotic sets.

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