Bifurcation analysis and chaos control of a discrete-time prey-predator model with fear factor
Ceyu Lei, Xiaoling Han, Weiming Wang
Abstract
In this paper, we investigate the complex dynamics of a classical discrete-time prey-predator system with the cost of anti-predator behaviors. We first give the existence and stability of fixed points of this system. And by using the central manifold theorem and bifurcation theory, we prove that the system will experience flip bifurcation and Neimark-Sacker bifurcation at the equilibrium points. Furthermore, we illustrate the bifurcation phenomenon and chaos characteristics via numerical simulations. The results may enrich the dynamics of the prey-predator systems.
Topics & Concepts
BifurcationMathematicsSaddle-node bifurcationTranscritical bifurcationBiological applications of bifurcation theoryCenter manifoldApplied mathematicsPredatorControl theory (sociology)Bifurcation diagramBifurcation theoryStability (learning theory)PredationCHAOS (operating system)Complex dynamicsInfinite-period bifurcationHomoclinic bifurcationMathematical analysisHopf bifurcationControl (management)Computer sciencePhysicsEcologyArtificial intelligenceBiologyNonlinear systemComputer securityMachine learningQuantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Dynamics and Pattern FormationAdvanced Differential Equations and Dynamical Systems