Coupling inhibitory populations: from phase-locking to chaos

Synchronization of neural oscillations has been hypothesized to play an essential role in the large-scale inte-gration of the activity of distinct cell assemblies in brain. Experiments consistently show that synchronous periodic rhythms emerge, disappear and organize themselves spatially across multiple local areas, oscillat-ing coherently with dynamically evolving phase relations [1]. The strong irregularity of cortical neurons response in vivo combined with a significant degree of synchrony in the temporal fluctuations of neuronal activities hints as well to the existence of less regular oscillatory episodes, possibly associated to intrinsically chaotic dynamical states [2]. In this work we explain in a unified way the generation of local oscillatory ac-tivity in inhibitory interneuronal networks, the spontaneous development of phase-locked configurations in networks with patchy connections, and, finally, the transition from periodic to aperiodic oscillatory regimes [3, 4]. We first studied a simplified model in which a local network of neurons is represented by a threshold-linear firing rate variable inhibiting itself with a delay [4]. Delayed inhibition leads to oscillations of the firing rate, provided that the self-coupling is strong enough. Two such oscillating units are then coupled together symmetrically. Periodic in-phase and out-of-phase oscillations as well as bistable states can be obtained if there is reciprocal inhibition between the units. On the other hand, when the reciprocal interaction i