STABILITY AND BIFURCATION IN A PREDATOR–PREY MODEL WITH PREY REFUGE
WENCHANG CHEN, Hengguo Yu, Chuanjun Dai, QING GUO, HE LIU, Min Zhao
Abstract
In this paper, a predator–prey model with prey refuge was developed to investigate how prey refuge affect the dynamics of predator–prey interaction. We studied the existence and stability of equilibria, and then derived the sufficient conditions for the bifurcation such as saddle-node, transcritical, Hopf and Bogdanov–Takens bifurcation. In addition, a series of numerical simulations were carried out to illustrate the theoretical analysis, and the numerical results are consistent with the analytical results. Our results demonstrate that prey refuge has a great impact on the predator–prey dynamics.
Topics & Concepts
PredationBifurcationPredatorHopf bifurcationMathematicsStability (learning theory)Applied mathematicsControl theory (sociology)EcologyComputer sciencePhysicsBiologyNonlinear systemArtificial intelligenceControl (management)Quantum mechanicsMachine learningMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsMathematical Biology Tumor Growth