Coexisting attractors, chaos control and synchronization in a self-exciting homopolar dynamo system

Abstract

PurposeThe purpose of this paper is to investigate coexisting attractors, chaos control and synchronization in a self-exciting homopolar dynamo system in this paper.Design/methodology/approachTwo single controllers are designed and added to the proposed 3D autonomous chaotic system, and its stability at zero equilibrium point is guaranteed by applying an appropriate control signal based on the Lyapunov stability theory.FindingsNumerical simulations reveal that the proposed 3D dynamo system exhibits periodic oscillations, double-scroll chaotic attractors and coexisting attractors. Finally, a single controller is designed for the global asymptotic synchronization of a unidirectionally coupled identical 3D autonomous chaotic system.Originality/valueThe derived results of this paper are new and complement some earlier works. The innovation concludes two points in this paper; coexisting attractors are foundthe and an appropriate control signal based on the Lyapunov stability theory is established. The ideas of this paper can be applied to investigate some other homopolar dynamo systems.