This study investigates the dynamics of the Lorenz hyperchaotic system and presents an active control-based synchronization approach for two identical systems. To confirm the hyperchaotic nature of the system, an examination of its dynamic structure is conducted, emphasizing Lyapunov exponents, phase-space evolution, and sensitivity to initial conditions. Subsequently, a synchronization scheme operating as a driver-response is introduced. The associated error dynamics are employed to evaluate the stability of the synchronization process, and the influence of control parameters on convergence conditions and system eigenvalues is analyzed. It is examined that a signal masking and recovery application to show that the proposed method goes beyond just theoretical study. Before and after the controller is turned on, the system's behavior is checked. After synchronization, the masked signal can be used to accurately reconstruct the transmitted signal. The use of different input signals also evaluates the consistency of the proposed method. The proposed method maintains effective performance under various conditions, as each case exhibits similar dynamical behavior. These results collectively demonstrate that the synchronization framework based on active control offers a feasible and dependable solution for the Lorenz hyperchaotic system.
Tunç et al. (Sat,) studied this question.