Persistence and bifurcation analysis among four species interactions with the influence of competition, predation and harvesting
Shireen Jawad, Marwa Al Nuaimi
Abstract
In this paper, the interplay among four population species is offered. The system consists of two competitive prey, predator and super predators. The application of the hypothesis of the Sotomayor theorem for local bifurcation around every equilibrium point is adopted. It is detected that the transcritical bifurcation could occur near most of the system's equilibrium points, while saddle-node and pitchfork bifurcation can not be accrued at any of them. Further, the conditions that guarantee the accruing Hopf bifurcation are carried out. Finally, some numerical analysis is illustrated to confirm the analytical results.
Topics & Concepts
Pitchfork bifurcationSaddle-node bifurcationTranscritical bifurcationBogdanov–Takens bifurcationPredationMathematicsBifurcationHopf bifurcationPopulationEquilibrium pointPersistence (discontinuity)Biological applications of bifurcation theoryCompetition (biology)Control theory (sociology)Applied mathematicsMathematical economicsMathematical analysisEcologyBiologyPhysicsEconomicsDemographyNonlinear systemEngineeringControl (management)Differential equationManagementGeotechnical engineeringQuantum mechanicsSociologyMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsEvolutionary Game Theory and Cooperation