Dissertation Defense: Arnab Dey Sarkar

Mathematics student Arnab Dey Sarkar's dissertation is titled "Bistability analysis of excitatory, inhibitory and somatostatin neuron network". Rhythmic activity is a fundamental feature of cortical networks and is believed to support sensory processing, cognition, and motor control. This thesis investigates how interactions among excitatory neurons and two inhibitory cell types—parvalbumin-positive (PV) and somatostatin-positive (SST) interneurons—shape cortical oscillations. Using spiking-network simulations, exact mean-field reduction, and bifurcation analysis, I show that a single circuit can support two distinct beta rhythms and can switch between them in response to transient inputs. The results also demonstrate that both inhibitory pathways are essential for this multirhythmic behavior and that modulation of SST activity can move the network into or out of these regimes. More broadly, this work shows how inhibitory diversity can generate multiple stable rhythms and complex oscillatory dynamics within a single cortical circuit. Advisor: Dr. Bard Ermentrout