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

Abdul Qadeer Khan | Zendy; Imtiaz Ahmad | Zendy; H. S. Alayachi | Zendy; Mohd Salmi Md Noorani | Zendy; Abdul Khaliq | Zendy

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

Author(s) -

Abdul Qadeer Khan,

Imtiaz Ahmad,

H. S. Alayachi,

Mohd Salmi Md Noorani,

Abdul Khaliq

Publication year - 2020

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2020317

Subject(s) - allee effect , lyapunov exponent , mathematics , chaotic , bifurcation , population , statistical physics , discrete time and continuous time , control theory (sociology) , fractal , hopf bifurcation , physics , mathematical analysis , nonlinear system , control (management) , computer science , statistics , demography , quantum mechanics , artificial intelligence , sociology

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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