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Covariant Lyapunov vectors for scale-free networks of Henon maps are highlylocalized. We revealed two mechanisms of the localization related to full andphase cluster synchronization of network nodes. In both cases the localizationnodes remain unaltered in course of the dynamics, i.e., the localization isnonwandering. Moreover this is predictable: the localization nodes are found tohave specific dynamical and topological properties and they can be foundwithout computing of the covariant vectors. This is an example of explicitrelations between the system topology, its phase space dynamics, and theassociated tangent space dynamics of covariant Lyapunov vectors.

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