Dynamics of coupled neural populations: The role of synaptic dynamics

In this paper, we study the dynamics of two recent mean-field models representing the behavior of heterogeneous all-to-all coupled quadratic integrate-and-fire neural networks. The main difference between both models is that one considers the influence of the synaptic dynamics mechanism on the macroscopic dynamics, while the other does not. The latter model can be considered the limiting case of the former. In the literature, it has been shown, without a detailed explanation, that significant changes in the dynamics occur as synaptic dynamics increases (in the studied parametric region when considering the coupling of one excitatory and one inhibitory population): chaotic behavior disappears (or it is less frequent) and bursting dynamics emerge. The existence of synaptic dynamics, which allows a delay in synaptic transmission, seems to reduce the emergence of chaotic dynamics by increasing the synaptic time constant and maintains a phase-locked state in the form of bursting dynamics in the mean-field model. In this article, we examine in depth the different dynamical behaviors that can be found in both mean-field models (spiking, bursting, and Rössler-like chaotic behaviors) and study in detail the bifurcations underlying their appearance and disappearance. Moreover, we relate the disappearance of various behaviors with the recently introduced geometric bifurcations. Thus, our analyses provide a global view of the dynamical landscape, providing insights into the role of synaptic dynamics in coupled neural populations.