A 3D chaotic system with dissipative and conservative behaviors and its control using two linear active controllers

Abstract

Complexity of a chaotic system is defined with respect to its Lyapunov dimension. As the Lyapunov dimension for a chaotic system increases, so does its complexity. The Lyapunov dimension of a dissipative chaotic system is represented by a real number. Whereas, for a chaotic system with conservative flow, it is always an integer and is equal to the order of the chaotic system. This paper explores the dissipative and conservative natures of an available dissipative chaotic system with the help of the Lyapunov dimension. Finally, an active linear controller is designed to stabilize both the dissipative and conservative behaviors of the chaotic system. Only two control inputs in two states are used for this purpose. The simulation results reveal that the objectives of the paper are successfully achieved.