Complex dynamics and bifurcation analysis for a Beverton–Holt population model with Allee effect
Karima Mokni, Mohamed Ch-Chaoui
Abstract
In this paper, we have derived a discrete evolutionary Beverton–Holt population model. The model is built using evolutionary game theory methodology and takes into consideration the strong Allee effect related to predation saturation. We have discussed the existence of the positive fixed point and examined its asymptotic stability. Analytically, we demonstrated that the derived model exhibits Neimark–Sacker bifurcation when the maximal predator intensity is at lower values. All chaotic behaviors are justified numerically. Finally, to avoid these chaotic features and achieve asymptotic stability, we implement two chaos control methods.
Topics & Concepts
Allee effectMathematicsApplied mathematicsChaoticPopulationLeslie matrixPopulation modelHopf bifurcationBifurcationStability (learning theory)Control theory (sociology)Exponential stabilityEquilibrium pointMathematical economicsStatistical physicsMathematical analysisNonlinear systemComputer sciencePhysicsDifferential equationControl (management)SociologyMachine learningQuantum mechanicsDemographyArtificial intelligenceMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsEvolutionary Game Theory and Cooperation