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Discrete-time predator-prey model with flip bifurcation and chaos control

1 Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
2 Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur-10250 (AJK), Pakistan
3 School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia
4 Department of Mathematics, Riphah International University, Lahore Campus, Lahore, Pakistan

Special Issues: Numerical Linear Algebra for Large-Scale Dynamical Systems

We explore the local dynamics, flip bifurcation, chaos control and existence of periodic point of the predator-prey model with Allee effect on the prey population in the interior of $\mathbb{R}^*{_+^2}$. Nu-merical simulations not only exhibit our results with the theoretical analysis but also show the complex dynamical behaviors, such as the period-2, 8, 11, 17, 20 and 22 orbits. Further, maximum Lyapunov exponents as well as fractal dimensions are also computed numerically to show the presence of chaotic behavior in the model under consideration.
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© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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