Dynamics of Holling-type II prey–predator system with a protection zone for prey
Aung Zaw Myint, Mingxin Wang
Abstract
In this paper, a diffusive predator–prey model with Holling type II (Michaelis–Menten) functional response and a protection zone for prey is investigated. Dynamics and steady state solutions of the system are analyzed. We give the a priori estimates and obtain the nonexistence of nonconstant positive solution as the diffusion coefficients are large enough. Moreover, we demonstrate the existence and stability of nonconstant steady state solutions branching from constant semi-trivial solution by using bifurcation theory.
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MathematicsFunctional responseBifurcationPredationSteady state (chemistry)Constant (computer programming)Type (biology)Applied mathematicsStability (learning theory)A priori and a posterioriMathematical analysisControl theory (sociology)PredatorNonlinear systemPhysicsEcologyComputer sciencePhilosophyChemistryArtificial intelligenceMachine learningEpistemologyControl (management)BiologyProgramming languageQuantum mechanicsPhysical chemistryMathematical and Theoretical Epidemiology and Ecology ModelsMathematical Biology Tumor GrowthNonlinear Differential Equations Analysis