Analysis and Synchronization of a New Hyperchaotic System with Exponential Term

In this paper, a new four-dimensional hyperchaotic system with an exponential term is presented. The basic dynamical properties and chaotic behavior of the new attractor are analyzed. It can be shown that this system possesses either a line of equilibria or a single one. The existence of hyperchaos is confirmed by its Lyapunov exponents. Moreover, the synchronization problem for the hyperchaotic system is studied. Based on the Lyapunov stability theory, an adaptive control law with two inputs is proposed to achieve the global synchronization. Numerical simulations are given to validate the correctness of the proposed control law.

Automated summary

This paper presents a new four-dimensional hyperchaotic system with an exponential term and analyzes its basic dynamical properties and chaotic behavior, confirming the existence of hyperchaos. The synchronization problem for the hyperchaotic system is studied, and an adaptive control law with two inputs is proposed based on Lyapunov stability theory to achieve global synchronization. Numerical simulations validate the proposed control law's correctness.