Stability of the 3-torus solution in a ring of coupled Duffing oscillators
Ł. Borkowski, Andrzej Stefański
Abstract
Abstract The dynamics of the ring of unidirectionally coupled single-well Duffing oscillators is analyzed in numerical simulation for identical nodal oscillators. The research is concentrated on the existence of the stable 3D torus attractor in this system. It is shown that 3-frequency quasi-periodicity can be robustly stable in wide range of parameters of the system under consideration. As an explanation of this stability, the conjecture on the coexistence and superposition of two independent effects characterized with irrational frequencies, i.e., the classical Newhouse, Ruelle and Takens scenario and rotating wave flow, is formulated.
Topics & Concepts
TorusAttractorSuperposition principleRing (chemistry)MathematicsStability (learning theory)ConjectureFlow (mathematics)Duffing equationMathematical analysisRange (aeronautics)Control theory (sociology)PhysicsPure mathematicsGeometryNonlinear systemComputer scienceQuantum mechanicsMachine learningComposite materialMaterials scienceArtificial intelligenceControl (management)Organic chemistryChemistryNonlinear Dynamics and Pattern FormationChaos control and synchronizationQuantum chaos and dynamical systems