A novel simple 5D hyperchaotic system derived from the 3D Sprott C system

Abstract

A novel simple 5D hyperchaotic system with two non-hyperbolic equilibria points is presented. The proposed system is designed by coupling between a 3D Sprott C system and a 2D linear system via a coupling strategy. Compared to the traditional systems, a new system is considered simply because it consists of five first-order ordinary differential equations with nine terms: seven linear terms and two quadratic nonlinearities. Due to the nature of equilibria points, this system belongs to the group of self-excited attractors. The attractors have been described as hyperchaotic. Finally, the projective synchronization problem of the new system has been realized through both Lyapunov stability theory and numerical simulation. The numerical simulation confirmed the validity of our analytical results. This work throws light on the great significance of the new system via designing controllers with the minimum terms possible are helpful in some practical applications.