  We study a pulse-coupled dynamics of excitable elements in uncorrelated
scale-free networks. Regimes of self-sustained activity are found for
homogeneous and inhomogeneous couplings, in which the system displays a wide
variety of behaviors, including periodic and irregular global spiking signals,
as well as coherent oscillations, an unexpected form of synchronization. Our
numerical results also show that the properties of the population firing rate
depend on the size of the system, particularly its structure and average value
over time. However, a few straightforward dynamical and topological strategies
can be introduced to enhance or hinder these global behaviors, rendering a
scenario where signal control is attainable, which incorporates a basic
mechanism to turn off the dynamics permanently. As our main result, here we
present a framework to estimate, in the stationary state, the mean firing rate
over a long time window and to decompose the global dynamics into average
values of the inter-spike-interval of each connectivity group. Our approach
provides accurate predictions of these average quantities when the network
exhibits high heterogeneity, a remarkable finding that is not restricted
exclusively to the scale-free topology.
