Desynchronization in diluted neural networks

The dynamical behavior of a weakly diluted fully inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochasticlike 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 stochasticlike behavior is 'limited' to an exponentially long (with the system size) transient. Remarkably, the transient dynamics turns out to be stationary.