Stability and Bifurcation Analysis of a Beddington–DeAngelis Prey–Predator Model with Fear Effect, Prey Refuge and Harvesting
Jiao-Guo Wang, Xin-You Meng, Long Lv, Jie Li
Abstract
In this paper, a Beddington–DeAngelis prey–predator model with fear effect, refuge and harvesting is investigated. First, the positivity of solutions and boundedness of system are given. Then, the existence and local stability of equilibria of such system are obtained. Next, not only different codimension-one bifurcations, such as saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation take place, but also Bogdanov–Takens bifurcation of codimension-two occurs as predicted by the center manifold theorem and bifurcation theory. Finally, some numerical simulations are carried out to confirm our theoretical results.
Topics & Concepts
Center manifoldMathematicsTranscritical bifurcationSaddle-node bifurcationBogdanov–Takens bifurcationBifurcationPitchfork bifurcationBiological applications of bifurcation theoryCodimensionApplied mathematicsControl theory (sociology)Hopf bifurcationHomoclinic bifurcationStability (learning theory)Mathematical analysisComputer sciencePhysicsNonlinear systemControl (management)Machine learningArtificial intelligenceQuantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsAdvanced Differential Equations and Dynamical Systems