Codimension two 1:1 strong resonance bifurcation in a discrete predator-prey model with Holling Ⅳ functional response
Mianjian Ruan, Chang Li, Xianyi Li
Abstract
<abstract><p>In this paper we revisit a discrete predator-prey model with Holling Ⅳ functional response. By using the method of semidiscretization, we obtain new discrete version of this predator-prey model. Some new results, besides its stability of all fixed points and the transcritical bifurcation, mainly for codimension two 1:1 strong resonance bifurcation, are derived by using the center manifold theorem and bifurcation theory, showing that this system possesses complicate dynamical properties.</p></abstract>
Topics & Concepts
Functional responseCodimensionMathematicsBifurcationCenter manifoldPredationTranscritical bifurcationSaddle-node bifurcationPredatorBifurcation theoryDiscrete time and continuous timeMathematical analysisApplied mathematicsPure mathematicsHopf bifurcationPhysicsNonlinear systemStatisticsBiologyPaleontologyQuantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsAdvanced Differential Equations and Dynamical SystemsDifferential Equations and Numerical Methods