Stable chaos in fluctuation driven neural circuits

We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare mean ver- sus fluctuations driven networks, the former (latter) is realized by considering purely excit- atory (inhibitory) sparse neural circuits. In the excitatory case the instabilities of the system can be completely captured by an usual linear stability (Lyapunov) analysis, whereas the inhibitory networks can display the coexistence of linear and nonlinear insta- bilities. The nonlinear effects are associated to finite amplitude instabilities, which have been characterized in terms of suitable indicators. For inhibitory coupling one observes a transition from chaotic to non chaotic dynamics by decreasing the pulse-width. For suffi- ciently fast synapses the system, despite showing an erratic evolution, is linearly stable, thus representing a prototypical example of stable chaos.