Predictable nonwandering localization of covariant Lyapunov vectors and cluster synchronization in scale-free networks of chaotic maps

Abstract

Covariant Lyapunov vectors for scale-free networks of Henon maps are highly localized. We revealed two mechanisms of the localization related to full and phase cluster synchronization of network nodes. In both cases the localization nodes remain unaltered in course of the dynamics, i.e., the localization is nonwandering. Moreover this is predictable: the localization nodes are found to have specific dynamical and topological properties and they can be found without computing of the covariant vectors. This is an example of explicit relations between the system topology, its phase space dynamics, and the associated tangent space dynamics of covariant Lyapunov vectors.