Dynamical analysis, synchronization, circuit design, and secure communication of a novel hyperchaotic system

Abstract

This paper is devoted to introduce a novel fourth-order hyperchaotic system. The hyperchaotic system is constructed by adding a linear feedback control level based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers. The local dynamical entities, such as the basic dynamical behavior, the divergence, the eigenvalue, and the Lyapunov exponents of the new hyperchaotic system, are all investigated analytically and numerically. Then, an active control method is derived to achieve global chaotic synchronization of the novel hyperchaotic system through making the synchronization error system asymptotically stable at the origin based on Lyapunov stability theory. Next, the proposed novel hyperchaotic system is applied to construct another new hyperchaotic system with circuit deformation and design a new hyperchaotic secure communication circuit. Furthermore, the implementation of two novel electronic circuits of the proposed hyperchaotic systems is presented, examined, and realized using physical components. A good qualitative agreement is shown between the simulations and the experimental results around 500 kHz and below 1 MHz.