  Experimental studies of synchronization properties on networks with
controlled connection topology can provide powerful insights into the physics
of complex networks. Here, we report experimental results on the influence of
connection topology on synchronization in fiber-optic networks of chaotic
optoelectronic oscillators. We find that the recently predicted non-monotonic,
cusp-like synchronization landscape manifests itself in the rate of convergence
to the synchronous state. We also observe that networks with the same number of
nodes, same number of links, and identical eigenvalues of the coupling matrix
can exhibit fundamentally different approaches to synchronization. This
previously unnoticed difference is determined by the degeneracy of associated
eigenvectors in the presence of noise and mismatches encountered in real-world
conditions.
