Dynamical Analysis of a Delayed Diffusive Predator–Prey Model with Additional Food Provided and Anti-Predator Behavior
Ruizhi Yang, Xiao Hong Zhao, Yong An
Abstract
We studied a delayed predator–prey model with diffusion and anti-predator behavior. Assume that additional food is provided for predator population. Then the stability of the positive equilibrium is considered. The existence of Hopf bifurcation is also discussed based on the Hopf bifurcation theory. The property of Hopf bifurcation is derived through the theory of center manifold and normal form method. Finally, we analyze the effect of time delay on the model through numerical simulations.
Topics & Concepts
Center manifoldHopf bifurcationPredatorPredationMathematicsStability (learning theory)PopulationApplied mathematicsFunctional responseSaddle-node bifurcationBifurcationControl theory (sociology)Mathematical analysisEcologyPhysicsEconomicsBiologyComputer scienceNonlinear systemDemographyManagementMachine learningQuantum mechanicsControl (management)SociologyMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsMathematical Biology Tumor Growth