Stability of a fear effect predator–prey model with mutual interference or group defense
Mengxin He, Zhong Li
Abstract
In this paper, we consider a fear effect predator-prey model with mutual interference or group defense. For the model with mutual interference, we show the interior equilibrium is globally stable, and the mutual interference can stabilize the predator-prey system. For the model with group defense, we discuss the singular dynamics around the origin and the occurrence of Hopf bifurcation, and find that there is a separatrix curve near the origin such that the orbits above which tend to the origin and the orbits below which tend to limit cycle or the interior equilibrium.
Topics & Concepts
PredationPredatorInterference (communication)Hopf bifurcationLimit cycleStability (learning theory)Group (periodic table)BifurcationLimit (mathematics)Control theory (sociology)MathematicsBiologyEconomicsPhysicsEcologyMathematical analysisComputer scienceNonlinear systemTelecommunicationsChannel (broadcasting)Machine learningManagementControl (management)Quantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsEvolutionary Game Theory and Cooperation