Mendoza C, Boccaletti S, Politi A “Convective instabilities of synchronization manifolds in spatially extended systems”. Phys. Rev. E. 69 (4) 047202 Part 2, (2004).
We study the stability properties of anticipating synchronization in an open chain of unidirectionally coupled
identical chaotic oscillators. Despite being absolutely stable, the synchronization manifold is unstable to propagating
perturbations. We analyze and characterize such instabilities drawing a qualitative and quantitative
comparison with the convective instabilities typical of spatially extended systems.