  This work addresses synchronization in transient, non-linear stochastic
dynamics corresponding to accesses performed by self-avoiding walks originating
at each node of a complex network. More specifically, the synchronizability of
accesses incoming from other nodes has been considered and quantified in terms
of the entropy of the mean periods of access, being closely associated to the
efficiency of access delivery to each node. The concept of synchronous support
of a node $i$ has also been suggested as corresponding to the nodes which
contribute the most for the synchronization of the accesses to $i$. These
concepts have been applied to the analysis of 6 networks of different types,
leading to markedly smaller synchronizability being obtained for the
Watts-Strogatz and a geographical models. The more uniform synchronizabilities
were identified for the Watts-Strogatz and path-regular structures. Varying
degrees of correlations were found between the synchronizability and the degree
or outward accessibility of the nodes. The synchronous support of a node $i$
has been found to present diverse structure, including nodes which may be near
to $i$, or nodes which are scattered through the network and far away from $i$.
