A diffusive predator-prey model with generalist predator and time delay
Ruizhi Yang, Dan Jin, Wenlong Wang
Abstract
<abstract><p>Time delay in the resource limitation of the prey is incorporated into a diffusive predator-prey model with generalist predator. By analyzing the eigenvalue spectrum, time delay inducing instability and Hopf bifurcation are investigated. Some conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation. The results suggest that time delay can destabilize the stability of coexisting equilibrium and induce bifurcating periodic solution when it increases through a certain threshold.</p></abstract>
Topics & Concepts
Hopf bifurcationCenter manifoldMathematicsPredatorBifurcationEigenvalues and eigenvectorsStability (learning theory)PredationApplied mathematicsGeneralist and specialist speciesInstabilityFunctional responseDelay differential equationMathematical analysisControl theory (sociology)Differential equationPhysicsEconomicsComputer scienceEcologyBiologyMechanicsMachine learningQuantum mechanicsNonlinear systemControl (management)HabitatManagementMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Differential Equations AnalysisEvolution and Genetic Dynamics