A novel simple saddle-foci equilibria 4D hyperchaotic system

This paper presents a 4D hyperchaotic system with two unstable saddle-foci equilibria which is constructed by combining a 3D chaotic system with a 1D linear system utilizing a coupling control strategy. The proposed system is characterized by one exponential term and consists of eight terms. Some of the dynamic behaviors of this system have been analyzed theoretically and numerically through simulation such as equilibria points, Lyapunov exponents, Kaplan-York dimension, Multistability, chaos control, and chaos synchronization. The proposed controls were implemented theoretically through the Lyapunov stability theorem and the numerical simulation confirmed the accuracy and validity of our theoretical results.