  We studied, both analytically and numerically, complex excitable networks, in
which connections are time dependent and some of the nodes remain silent at
each time step. More specifically, (a) there is a heterogenous distribution of
connection weights and, depending on the current degree of order, some
connections are reinforced/weakened with strength Phi on short-time scales, and
(b) only a fraction rho of nodes are simultaneously active. The resulting
dynamics has attractors which, for a range of Phi values and rho exceeding a
threshold, become unstable, the instability depending critically on the value
of rho. We observe that (i) the activity describes a trajectory in which the
close neighborhood of some of the attractors is constantly visited, (ii) the
number of attractors visited increases with rho, and (iii) the trajectory may
change from regular to chaotic and vice versa as rho is, even slightly
modified. Furthermore, (iv) time series show a power-law spectra under
conditions in which the attractors' space is most efficiently explored. We
argue on the possible qualitative relevance of this phenomenology to networks
in several natural contexts.
