Dynamical analysis and anti-synchronization of a new 6D model with self-excited attractors

• Published in: Applied Mathematics-A Journal of Chinese Universities Vol. 38; no. 1; pp. 27 - 43
• Main Authors: Al-Azzawi, Saad Fawzi, Al-Obeidi, Ahmed S.
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 01-03-2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Circuits; Controllers; Critical point; Dynamic characteristics; Liapunov exponents; Linearization; Mathematical models; Mathematics; Mathematics and Statistics; Nonlinear control; Stability analysis; Synchronism; Unstable equilibrium point; 37C75; 6D hyperchaotic system; anti-synchronization; Lyapunov stability theory; 34D08; self-excited attractor; 34D06
• ISSN: 1005-1031; 1993-0445
• DOI: 10.1007/s11766-023-3960-0

A novel 6D dissipative model with an unstable equilibrium point is introduced herein. Some of the dynamic characteristics of the proposed model were explored via analyses and numerical simulations including critical points, stability, Lyapunov exponents, time phase portraits, and circuit implementation. Also, anti-synchronization phenomena were implemented on the new system. Firstly, the error dynamics is found. Then, four different controllers are adopted to stabilize this error relying on the nonlinear control technique with two main ways: linearization and Lyapunov stability theory. In comparison with previous works, the present controllers realize anti-synchronization based on another method/linearization method. Finally, a comparison between the two ways was made. The simulation results show the effectiveness and accuracy of the first analytical strategy.