Qualitative behavior of a two‐dimensional discrete‐time prey–predator model
Messaoud Berkal, Juan F. Navarro
Abstract
In this article, we discuss the qualitative behavior of a two-dimensional discrete-time prey-predator model. This system is the result of the application of a nonstandard difference scheme to a system of differential equations for a prey-predator model including intraspecific competition of prey population. In particular, we evaluate the fixed points of the system and study their local asymptotic stability. We also prove the existence of a Neimark-Sacker bifurcation.
Topics & Concepts
Intraspecific competitionMathematicsPredationApplied mathematicsBifurcationPopulation modelPopulationStability (learning theory)Discrete time and continuous timePredatorDifferential equationCompetition (biology)Mathematical analysisStatisticsEcologyComputer scienceNonlinear systemBiologyPhysicsDemographyMachine learningSociologyQuantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsNonlinear Dynamics and Pattern Formation