  Pattern formation and evolution in unsynchronizable complex networks are
investigated. Due to the asymmetric topology, the synchronous patterns formed
in complex networks are irregular and nonstationary. For coupling strength
immediately out of the synchronizable region, the typical phenomenon is the
on-off intermittency of the system dynamics. The patterns appeared in this
process are signatured by the coexistence of a giant cluster, which comprises
most of the nodes, and a few number of small clusters. The pattern evolution is
characterized by the giant cluster irregularly absorbs or emits the small
clusters. As the coupling strength leaves away from the synchronization
bifurcation point, the giant cluster is gradually dissolved into a number of
small clusters, and the system dynamics is characterized by the integration and
separation of the small clusters. Dynamical mechanisms and statistical
properties of the nonstationary pattern evolution are analyzed and conducted,
and some scalings are newly revealed. Remarkably, it is found that the few
active nodes, which escape from the giant cluster with a high frequency, are
independent of the coupling strength while are sensitive to the bifurcation
types. We hope our findings about nonstationary pattern could give additional
understandings to the dynamics of complex systems and have implications to some
real problems where systems maintain their normal functions only in the
unsynchronizable state.
