Bursting in a next generation neural mass model with synaptic dynamics: a slow–fast approach

Abstract We report a detailed analysis on the emergence of bursting in recently developed neural mass model that includes short-term synaptic plasticity. Neural models can mimic collective dynamics large-scale neuronal populations terms few macroscopic variables like mean membrane potential and firing rate. The present one is particularly important, as it represents an exact meanfield limit synaptically coupled quadratic integrate fire (QIF) neurons. Without dynamics, periodic external current with slow frequency $$\varepsilon $$ ? lead to burst-like dynamics. patterns be understood using singular perturbation theory, specifically slow–fast dissection. With timescale separation leads variety phenomena their role for becomes inordinately more intricate. Canards are crucial understand route bursting. They describe trajectories evolving nearby repelling locally invariant sets system exist at transition between subthreshold Near = 0$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">?=0 , we peculiar jump-on canards which block continuous In biologically plausible -regime, this bursts emerge via consecutive spike-adding transitions. onset complex involves mixed-type-like torus form very first spikes burst follow fast-subsystem cycles. numerically evidence same mechanisms responsible QIF network plastic synapses. main conclusions apply network, owing exactness limit.