Open AccessDiscrete-time predator-prey model with flip bifurcation and chaos control
Author(s) -
A. Q. 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 , bifurcation , chaotic , statistical physics , population , control theory (sociology) , population model , fractal , hopf bifurcation , discrete time and continuous time , complex dynamics , mathematical analysis , physics , nonlinear system , control (management) , computer science , statistics , quantum mechanics , artificial intelligence , demography , 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.