  Inhibitory neurons play a crucial role in maintaining persistent neuronal
activity. Although connected extensively through electrical synapses
(gap-junctions), these neurons also exhibit interactions through chemical
synapses in certain regions of the brain. When the coupling is sufficiently
strong, the effects of these two synaptic modalities combine in a nonlinear
way. Hence, in this work, we focus on the strong inhibition regime and identify
the parametric conditions that result in the emergence of self-sustained
oscillations in systems of coupled excitable neurons, in the presence of a
brief sub-threshold stimulus. Our investigation on the dynamics in a minimal
network of two neurons reveals a rich set of dynamical behaviors viz., periodic
and various complex oscillations including period-n (n=2,4,8...) dynamics and
chaos. We further extend our study by considering a system of inhibitory
neurons arranged in a one-dimensional ring topology and determine the optimal
conditions for sustained activity. Our work highlights the nonlinear dynamical
behavior arising due to the combined effects of gap-junctions and strong
synaptic inhibition, which can have potential implications in maintaining
robust memory patterns.
