Dynamics and Bifurcation Structure of a Mean-Field Model of Adaptive Exponential Integrate-and-Fire Networks

The study of brain activity spans diverse scales and levels of description and requires the development of computational models alongside experimental investigations to explore integrations across scales. The high dimensionality of spiking networks presents challenges for understanding their dynamics. To tackle this, a mean-field formulation offers a potential approach for dimensionality reduction while retaining essential elements. Here, we focus on a previously developed mean-field model of adaptive exponential integrate and fire (AdEx) networks used in various research work. We observe qualitative similarities in the bifurcation structure but quantitative differences in mean firing rates between the mean-field model and AdEx spiking network simulations. Even if the mean-field model does not accurately predict phase shift during transients and oscillatory input, it generally captures the qualitative dynamics of the spiking network's response to both constant and varying inputs. Finally, we offer an overview of the dynamical properties of the AdExMF to assist future users in interpreting their results of simulations.