Complex Dynamics Analysis of a Discrete Amensalism System with a Cover for the First Species
Qimei Zhou, Fengde Chen, Sijia Lin
Abstract
Of interest is the dynamics of the discrete-time amensalism model with a cover on the first species. We first obtain the existence and stability of fixed points and the conditions for the permanent coexistence of two species. Then we demonstrate the occurrence of flip bifurcation by using the central manifold theorem and bifurcation theory. A hybrid control strategy is used to control the flip bifurcation and stabilize unstable periodic orbits embedded in the complex attractor. Numerical simulation verifies the feasibility of theoretical analysis and reveals some novel and exciting dynamic phenomena.
Topics & Concepts
BifurcationAttractorCover (algebra)Stability (learning theory)Control theory (sociology)Manifold (fluid mechanics)Biological applications of bifurcation theorySaddle-node bifurcationMathematicsDynamics (music)Center manifoldStatistical physicsComplex dynamicsApplied mathematicsComputer scienceMathematical analysisControl (management)PhysicsEngineeringHopf bifurcationNonlinear systemArtificial intelligenceQuantum mechanicsAcousticsMechanical engineeringMachine learningNonlinear Dynamics and Pattern FormationChaos control and synchronizationQuantum chaos and dynamical systems