STABILITY AND BIFURCATION OF A PREDATOR–PREY SYSTEM WITH MULTIPLE ANTI-PREDATOR BEHAVIORS

Y. L. Xia, XINHAO HUANG, Fengde Chen, Lijuan Chen

2024Journal of Biological Systems12 citationsDOI

Abstract

In this paper, a predator–prey system with multiple anti-predator behaviors is developed and studied, where not only the prey may spread between patches but also the fear effect and counter-attack behavior of the prey are taken into account. First, the stability and existence of coexistence equilibria are presented. The unique positive equilibrium may be a saddle-node or a cusp of codimension 2. Then, various transversality conditions of bifurcations such as saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation are obtained. Moreover, compared with a single strategy, the multiple anti-predator strategies are more beneficial to the persistence and the population density of prey.

Topics & Concepts

Bogdanov–Takens bifurcationPredatorMathematicsSaddle-node bifurcationBifurcationTranscritical bifurcationPopulationBiological applications of bifurcation theoryPredationPitchfork bifurcationHopf bifurcationApplied mathematicsBifurcation diagramControl theory (sociology)Stability (learning theory)Allee effectEcologyBiologyNonlinear systemPhysicsComputer scienceDemographyMachine learningControl (management)Artificial intelligenceSociologyQuantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsEvolutionary Game Theory and Cooperation