RESUMO
This paper proposes a novel exponential hyper-chaotic system with complex dynamic behaviors. It also analyzes the chaotic attractor, bifurcation diagram, equilibrium points, Poincare map, Kaplan-Yorke dimension, and Lyapunov exponent behaviors. A fast terminal sliding mode control scheme is then designed to ensure the fast synchronization and stability of the new exponential hyper-chaotic system. Stability analysis was performed using the Lyapunov stability theory. One of the main features of the proposed controller is the finite time stability of the terminal sliding surface designed with high-order power function of error and derivative of error. The approach was implemented for image cryptosystem. Color image encryption was carried out to confirm the performance of the new hyper-chaotic system. For image encryption, the DNA encryption-based RGB algorithm was used. Performance assessment of the proposed approach confirmed the ability of the proposed hyper-chaotic system to increase the security of image encryption.