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 (AdEx) networks, utilized in various research works. We provide a systematic investigation of its properties and bifurcation structure, which was not available for this model. We show that this provides a comprehensive description and characterization of the model to assist future users in interpreting their results. The methodology includes model construction, stability analysis, and numerical simulations. Finally, we offer an overview of dynamical properties and methods to characterize the mean-field model, which should be useful for for other models.