Extending anticipation horizon of chaos synchronization schemes with time-delay coupling.

We analyse anticipating synchronization in chaotic systems with time-delay coupling. Two algorithms for extending the prediction horizon are considered. One of them is based on the design of a suitable coupling matrix compensating the phase lag in the time-delay feedback term of the slave system. The second algorithm extends the first by incorporating, in the coupling law, information from many previous states of the master and slave systems. We demonstrate the efficiency of both algorithms with the simple dynamical model of coupled unstable spirals, as well as with the coupled Rössler systems. The maximum prediction time attained for the Rössler system is equal to the characteristic period of chaotic oscillations.