Local sensitivity of spatiotemporal structures

We present an index for the local sensitivity of spatiotemporal structures in coupled oscillatory systems based on the asymptotic scaling of local-in-space, finite-time Lyapunov Exponents. For a system of nonlocally-coupled R"{o}ssler oscillators, we show that deviations of this index reflect the sensitivity to noise and the onset of spatial chaos for the patterns where coherence and incoherence regions coexist.