Bifurcation analysis of a two‐dimensional discrete‐time predator–prey model
M. Y. Hamada, Tamer El‐Azab, H. El-Metwally
Abstract
The dynamical behavior of a discrete predator–prey system with a nonmonotonic functional response is investigated in this work. We study the local asymptotic stability of the positive equilibrium of the system by examining the characteristic equation of the linearized system corresponding to the model. By choosing the growth rate as a bifurcation parameter, the existence of Neimark–Sacker and period‐doubling bifurcations at the positive equilibrium is established. Furthermore, the effects of perturbations on the system dynamics are investigated. Finally, examples are presented to illustrate our main results.
Topics & Concepts
MathematicsBifurcationDiscrete time and continuous timeSaddle-node bifurcationPeriod-doubling bifurcationApplied mathematicsTranscritical bifurcationBiological applications of bifurcation theoryPredationFunctional responseWork (physics)Stability (learning theory)Exponential stabilityBifurcation diagramControl theory (sociology)Mathematical analysisPredatorNonlinear systemStatisticsEcologyPhysicsEconomicsComputer scienceQuantum mechanicsMachine learningThermodynamicsBiologyControl (management)ManagementMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsNonlinear Dynamics and Pattern Formation