  We present an analytical framework that allows the quantitative study of
statistical dynamic properties of networks with adaptive nodes that have memory
and is used to examine the emergence of oscillations in networks with response
failures. The frequency of the oscillations was quantitatively found to
increase with the excitability of the nodes and with the average degree of the
network and to decrease with delays between nodes. For networks of networks,
diverse cluster oscillation modes were found as a function of the topology.
Analytical results are in agreement with large-scale simulations and open the
horizon for understanding network dynamics composed of finite memory nodes as
well as their different phases of activity.
