Long-time anticipation of chaotic states in time-delay coupled ring and linear arrays

We study the time-delay and unidirectionally coupled ring and linear arrays of chaotic systems, and find that under certain conditions, the linear array can spatial periodically “copy” the chaotic dynamics of the ring with very long anticipation times. Numerical calculations of the Lyapunov exponents show that the delay times can result in unsynchronized chaotic waves, periodic waves, and stable states in the ring that are replicated in the linear array, but have no effect on the absolute stability of the anticipatory synchronization. Our results show that such configurations can both enhance the absolute stability of the synchronization manifolds and minimize the effects of convective instabilities.