A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control**One of the authors (Dr. Zhouchao Wei) was supported by the National Natural Science Foundation of China (Grant No. 11772306).

Abstract

This paper presents a new four-dimensional (4D) autonomous chaotic system which has first Lyapunov exponent of about 22 and is comparatively larger than many existing three-dimensional (3D) and 4D chaotic systems. The proposed system exhibits hyperbolic curve and circular paraboloid types of equilibria. The system has all zero eigenvalues for a particular case of an equilibrium point. The system has various dynamical behaviors like hyperchaotic, chaotic, periodic, and quasi-periodic. The system also exhibits coexistence of attractors. Dynamical behavior of the new system is validated using circuit implementation. Further an interesting switching synchronization phenomenon is proposed for the new chaotic system. An adaptive global integral sliding mode control is designed for the switching synchronization of the proposed system. In the switching synchronization, the synchronization is shown for the switching chaotic, stable, periodic, and hybrid synchronization behaviors. Performance of the controller designed in the paper is compared with an existing controller.