Chaos synchronization in a hyperbolic dynamical system with long-range interactions

Abstract

We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. As a result, the numerically determined synchronization threshold agree with the analytical results previously obtained [C. Anteneodo et al., Phys. Rev. E 68, 045202(R) (2003)] for this class of systems. We present both careful numerical experiments and a rigorous mathematical explanation confirming this fact, allowing for a generalization involving hyperbolic coupled map lattices.