The interplay of inhibitory and electrical synapses results in complex persistent activity

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.