Complicate bifurcation behaviors of a discrete predator–prey model with group defense and nonlinear harvesting in prey
Wenbo Yao, Xianyi Li
Abstract
In this paper, some complicate dynamical behaviors are formulated for a discrete predator–prey model with group defense and nonlinear harvesting in prey. After considering the existence and stability for all of its nonnegative fixed points, our main work is to present those conditions for the occurrences of transcritical bifurcation, saddle-node bifurcation and Neimark–Sacker bifurcation, respectively. Numerical simulations not only verify the theoretical results for saddle-node bifurcation and Neimark–Sacker bifurcation but also display more interesting dynamical properties of the model.
Topics & Concepts
Saddle-node bifurcationMathematicsTranscritical bifurcationBifurcationBiological applications of bifurcation theoryPredationApplied mathematicsHeteroclinic bifurcationBifurcation theoryNonlinear systemBifurcation diagramPitchfork bifurcationStability (learning theory)Control theory (sociology)Computer scienceEcologyPhysicsControl (management)Machine learningArtificial intelligenceBiologyQuantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsMathematical Biology Tumor Growth