Quasi-optimal values in the Hamiltonian-based synchronization of chaotic systems

In this paper a quasi-optimal surface for the observer gain in a Hamiltonian-based controller with applications in chaos synchronization is reported. The synchronization scheme is based on a master-slave topology composed of two chaotic oscillators with identical parameters but by using different initial conditions. Therefore, a trade-off analysis on the synchronization regime and the observer gains (K) in an n-scroll chaotic system is obtained. Lyapunov exponents are not required to prove the stability of the synchronization error, which could expand the study to many others chaotic systems. The synchronization error can be obtained as lower than 0.0001 for certain types of permutations of K. Numerical simulations validate the theoretical background and the usefulness of the proposed approach.