  Spatio-temporal network dynamics is an emergent property of many complex
systems which remains poorly understood. We suggest a new approach to its study
based on the analysis of dynamical motifs -- small subnetworks with periodic
and chaotic dynamics. We simulate randomly connected neural networks and, with
increasing density of connections, observe the transition from quiescence to
periodic and chaotic dynamics. We explain this transition by the appearance of
dynamical motifs in the structure of these networks. We also observe domination
of periodic dynamics in simulations of spatially distributed networks with
local connectivity and explain it by absence of chaotic and presence of
periodic motifs in their structure.
