  The dynamic range measures the capacity of a system to discriminate the
intensity of an external stimulus. Such an ability is fundamental for living
beings to survive: to leverage resources and to avoid danger. Consequently, the
larger is the dynamic range, the greater is the probability of survival. We
investigate how the integration of different input signals affects the dynamic
range, and in general the collective behavior of a network of excitable units.
By means of numerical simulations and a mean-field approach, we explore the
nonequilibrium phase transition in the presence of integration. We show that
the firing rate in random and scale-free networks undergoes a discontinuous
phase transition depending on both the integration time and the density of
integrator units. Moreover, in the presence of external stimuli, we find that a
system of excitable integrator units operating in a bistable regime largely
enhances its dynamic range.

Neurons and Cognition;Disordered Systems and Neural Networks;Statistical Mechanics;Cellular Automata and Lattice Gases;Biological Physics