Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System
Sergey Kryzhevich, Виктор Аврутин, Gunnar Söderbacka
Abstract
In this paper, we study a classical two-predators-one-prey model. The classical model described by a system of three ordinary differential equations can be reduced to a one-dimensional bimodal map. We prove that this map has at most two stable periodic orbits. Besides, we describe the bifurcation structure of the map. Finally, we describe a mechanism that leads to bistable regimes. Taking this mechanism into account, one can easily detect parameter regions where cycles with arbitrary high periods or chaotic attractors with arbitrary high numbers of bands coexist pairwise.
Topics & Concepts
BistabilityMathematicsAttractorBifurcationPredationOrdinary differential equationChaoticPopulationCoupled map latticePairwise comparisonDifferential equationDynamics (music)Statistical physicsMathematical analysisApplied mathematicsPure mathematicsNonlinear systemControl theory (sociology)StatisticsEcologyPhysicsComputer scienceArtificial intelligenceSynchronization of chaosSociologyBiologyAcousticsQuantum mechanicsControl (management)DemographyMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Dynamics and Pattern FormationEvolution and Genetic Dynamics