Analysis of a two-timescale neuronal ring model with voltage-dependent,piecewise smooth inhibitory coupling

Recent technological advances allow for in-vivo and in-vitro observation of the activity of single neurons, neural ensembles, and complex brain networks, all in real-time. However, given the astonishing complexity of the brain, we rely on mathematical modelling and computational analysis to decode these experimental observations and uncover mechanisms that govern the neural systems of interest. The sheer breadth of this topic is overwhelming. It spans from simulating the dynamic interactions of ion channels, pumps and receptors in a single neuron to modelling the intricate interplay of neural populations at different temporal and spatial scales. To deal with this complexity, we make use of a diverse range of advanced mathematical tools, including control theory, phase reduction, and bifurcation analysis. This mini symposium will focus on novel mathematical methodologies and tools used for better understanding of the brain's neurocomputational landscape. We will showcase how these mathematical insights are applied to dissect specific neural circuits and decipher observed physiological phenomena. Our motivation is to showcase the synergy between theoretical and practical aspects of computational neuroscience. Through this synergy, we enhance our grasp of mathematical aspects of neurophysiology. Simultaneously, we demonstrate how observable brain phenomena inspire entirely new areas of mathematical analysis.