Mathematical analysis of a diffusive predator-prey model with herd behavior and prey escaping
Fethi Souna, Salih Djilali, Fayssal Charif
Abstract
In this paper, we consider a new approach of prey escaping from herd in a predator-prey model with the presence of spatial diffusion. First, the sensitivity of the equilibrium state density with respect to the escaping rate has been studied. Then, the analysis of the non diffusive system was investigated where boundedness, local, global stability, Hopf bifurcation are obtained. Besides, for the diffusive system, we proved the occurrence of Hopf bifurcation and the non existence of diffusion driven instability. Furthermore, the direction of Hopf bifurcation has been proved using the normal form on the center manifold. Some numerical simulations have been used to illustrate the obtained results.
Topics & Concepts
Hopf bifurcationCenter manifoldMathematicsPredationHerd behaviorInstabilityBifurcationStability (learning theory)Functional responseApplied mathematicsDiffusionPredatorManifold (fluid mechanics)Mathematical analysisStatistical physicsControl theory (sociology)PhysicsMechanicsEcologyNonlinear systemBiologyEconomicsThermodynamicsComputer scienceEngineeringManagementMachine learningQuantum mechanicsControl (management)Mechanical engineeringHerdingForestryGeographyMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsMathematical Biology Tumor Growth