Discrete-time predator-prey model with flip bifurcation and chaos control
Abdul Qadeer Khan, Imtiaz Ahmad, H. S. Alayachi, Mohd Salmi Md Noorani, Abdul Khaliq
Abstract
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.
Topics & Concepts
Allee effectLyapunov exponentMathematicsChaoticBifurcationPopulationStatistical physicsDiscrete time and continuous timeControl theory (sociology)FractalHopf bifurcationApplied mathematicsPhysicsMathematical analysisNonlinear systemControl (management)Computer scienceStatisticsQuantum mechanicsArtificial intelligenceSociologyDemographyMathematical and Theoretical Epidemiology and Ecology ModelsStochastic processes and statistical mechanicsEvolutionary Game Theory and Cooperation