Stable chaos in fluctuation driven neural circuits

•Nonlinear instabilities in fluctuation driven (balanced) neural circuits are studied.•Balanced networks display chaos and stable phases at different post-synaptic widths.•Linear instabilities coexists with nonlinear ones in the chaotic regime.•Erratic motion appears also in linearly stable phase due to stable chaos.

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 versus fluctuations driven networks, the former (latter) is realized by considering purely excitatory (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 instabilities. 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 sufficiently fast synapses the system, despite showing an erratic evolution, is linearly stable, thus representing a prototypical example of stable chaos.