The dynamical behaviour of a weakly diluted fully-inhibitory network of
pulse-coupled spiking neurons is investigated. Upon increasing the coupling
strength, a transition from regular to stochastic-like regime is observed. In
the weak-coupling phase, a periodic dynamics is rapidly approached, with all
neurons firing with the same rate and mutually phase-locked. The
strong-coupling phase is characterized by an irregular pattern, even though the
maximum Lyapunov exponent is negative. The paradox is solved by drawing an
analogy with the phenomenon of ``stable chaos'', i.e. by observing that the
stochastic-like behaviour is "limited" to a an exponentially long (with the
system size) transient. Remarkably, the transient dynamics turns out to be
stationary.Comment: 11 pages, 13 figures, submitted to Phys. Rev.