Dynamic analysis of a Leslie-Gower predator-prey model with the fear effect and nonlinear harvesting
Hongqiuxue Wu, Zhong Li, Mengxin He
Abstract
In this paper, we investigate the stability and bifurcation of a Leslie-Gower predator-prey model with a fear effect and nonlinear harvesting. We discuss the existence and stability of equilibria, and show that the unique equilibrium is a cusp of codimension three. Moreover, we show that saddle-node bifurcation and Bogdanov-Takens bifurcation can occur. Also, the system undergoes a degenerate Hopf bifurcation and has two limit cycles (i.e., the inner one is stable and the outer is unstable), which implies the bistable phenomenon. We conclude that the large amount of fear and prey harvesting are detrimental to the survival of the prey and predator.
Topics & Concepts
Bogdanov–Takens bifurcationHopf bifurcationBifurcationMathematicsCusp (singularity)Nonlinear systemSaddle-node bifurcationBistabilityBiological applications of bifurcation theoryAllee effectDegenerate energy levelsPredationStability (learning theory)Limit cyclePredatorTranscritical bifurcationPitchfork bifurcationApplied mathematicsHeteroclinic bifurcationLimit (mathematics)Mathematical analysisPhysicsEcologyComputer scienceGeometryBiologyPopulationDemographySociologyMachine learningQuantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsNonlinear Dynamics and Pattern Formation