The role of initial conditions in the synchronization problem

We show the numerical evidence of a case of desynchronized behaviour in two mutual y-coupled Chua's circuits with negative conditional Lyapunov exponents (CLE). In this case the synchronized state strongly depends on the initial conditions in the two circuits according to the shape of the basin of attraction. Crossing the basin's boundaries from synchronized to desynchronized phase, the maximum CLE, even showing a sharp transition, has always a negative value. We suggest two different ways to calculate the CLE to obtain more information about the desynchronized state.