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We investigate the dynamics of large stochastic networks with differenttimescales and nonlinear mean-field interactions. After deriving the limitequations for a general class of network models, we apply our results to thecelebrated Wilson-Cowan system with two populations with or without slowadaptation, paradigmatic example of nonlinear mean-field network. This systemhas the property that the dynamics of the mean of the solution exactlysatisfies an ODE. This reduction allows to show that in the mean-field limitand in multiple populations with multiple timescales, noise induces canardexplosions and Mixed-Mode Oscillations on the mean of the solution. This shedsnew light on the qualitative effects of noise and sensitivity to precise noisevalues in large stochastic networks. We further investigate finite-sizednetworks and show that systematic differences with the mean-field limits arisein bistable regimes (where random switches between different attractors occur)or in mixed-mode oscillations, were the finite-size effects induce early jumpsdue to the sensitivity of the attractor.

Noise-induced canard and mixed-mode oscillations in large stochastic networks with multiple timescales