Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system
Fi̇gen Kangalgi̇l, Seval Işık
Abstract
This article is about a discrete-time predator-prey model obtained by the forward Euler method. The stability of the fixed point of the model and the existence conditions of the Neimark-Sacker bifurcation are investigated. In addition, the direction of the Neimark-Sacker bifurcation is given. Moreover, OGY control method is to implement to control chaos caused by the Neimark-Sacker bifurcation. Finally, Neimark-Sacker bifurcation, chaos control strategy, and asymptotic stability of the only positive fixed point are verified with the help of numerical simulations. The existence of chaotic behavior in the model is confirmed by computing of the maximum Lyapunov exponents.
Topics & Concepts
MathematicsLyapunov exponentBifurcation diagramBifurcationFixed pointSaddle-node bifurcationDiscrete time and continuous timeApplied mathematicsBifurcation theoryTranscritical bifurcationPeriod-doubling bifurcationControl theory (sociology)ChaoticEuler methodEuler's formulaMathematical analysisControl (management)Nonlinear systemStatisticsComputer sciencePhysicsQuantum mechanicsArtificial intelligenceMathematical and Theoretical Epidemiology and Ecology ModelsChaos control and synchronizationNonlinear Dynamics and Pattern Formation