Discrete and Continuous Dynamical Systems - B · 2006 · 28 citations · 0 references
Natural SciencesAutonomous SystemsMathematicsDifferential EquationsDynamical SystemsSystem DynamicsBifurcation TheoryControl Of Dynamical SystemsControl TheoryNonlinear DynamicsPredator-prey InteractionsStability TheoryBifurcationBifurcation AnalysisBifurcation DiagramsImpulsive ControlImpulsive SystemsLambert W FunctionPhase PortraitsPredator-prey Models
The dynamics of a prey-predator model with impulsive state feedbackcontrol is studied by an autonomous system with impulses. Thedynamical behavior of this system is discussed by means of boththeoretical and numerical ways. The sufficient conditions ofexistence and stability of the semi-trivial periodic solution,positive period-one, and positive period-two solutions are obtainedby using Lambert W function and the analogue of thePoincaré criterion. The bifurcation analysis shows thatsolutions appear via a cascade of period-doubling in some intervalof parameters. The bifurcation diagrams, the Lyapunovexponents, and the phase portraits are given in two examples. Thediscussion of prey (pest) control strategy shows that the impulsivestate feedback control is effective.