Abstract—Synchronization of the broadband-like information-maskable state trajectories of the Lorenz-63 and Burke-Shaw chaotic systems is presented in this paper. The two systems are three-dimensional dissipative chaotic systems which have similar algebraic structures but are topologically nonequivalent. Active controllers were designed and employed to track the exponentially divergent information-masking signals of their state trajectories into synchrony, based on the Lyapunov stability criteria. Numerical simulation results via MATLAB 7 software confirmed the global synchronization of the systems for all initial conditions and the asymptotic stabilization of the resulting synchronization error dynamics in the sense of Lyapunov. In addition, the robustness of the generalized synchronization scheme to parametric perturbation in the nonlinear hyperbolic structure of the Burke-Shaw slave system when interchanged between sinh and cosh holds possibility for online tuning of the coupled systems to vary the broadband spectrum density of the information-masking carrier when applied to modelling and design of chaos-based secure communication systems.

 

Index Terms—lorenz-63 system, burke-shaw system, synchronization, active control, lyapunov stability

Cite: Edwin A. Umoh, "Generalized Synchronization of Topologically-Nonequivalent Chaotic Signals via Active Control," International Journal of Signal Processing Systems, Vol. 2, No. 2, pp. 139-143, December 2014. doi: 10.12720/ijsps.2.2.139-143