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

TL;DR

This paper investigates the conditions for complete synchronization in a lattice of coupled non-smooth chaotic maps, providing analytical and numerical validation that the synchronization threshold is governed by linear stability analysis.

Contribution

It offers a rigorous mathematical explanation for synchronization thresholds in hyperbolic coupled map lattices, extending previous results and confirming numerical findings.

Findings

Synchronization threshold matches analytical predictions

Linear stability determines synchronization in hyperbolic systems

Results generalize to hyperbolic coupled map lattices

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.