Stability and bifurcation analysis of discrete predator–prey model with nonlinear prey harvesting and prey refuge
Qing Shu, Jingli Xie
Abstract
In this paper, a discrete Leslie–Gower model with nonlinear prey harvesting and prey refuge is proposed. We prove the existence and stability of an interior equilibrium of the model. In addition, the existence of flip bifurcation and Neimark–Sacker bifurcation at the interior equilibrium is studied by applying central manifold theory and bifurcation theory. Using Pontryagin's maximum principle, we propose an optimal harvesting problem.
Topics & Concepts
MathematicsPredationCenter manifoldBifurcationApplied mathematicsTranscritical bifurcationNonlinear systemStability (learning theory)Control theory (sociology)Pontryagin's minimum principleBifurcation theoryMathematical economicsHopf bifurcationMathematical optimizationOptimal controlEcologyEconomicsComputer scienceMachine learningControl (management)PhysicsManagementQuantum mechanicsBiologyMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsNonlinear Dynamics and Pattern Formation