How bifurcations affect functional connectivity in finite-size neural networks

Understanding how the functional connectivity of a neural network (i.e. the statistical dependencies among different neurons) depends upon its anatomical connec-tivity and how it is modulated by other network para-meters is a central topic in neuroscience [1]. However, only few analytical investigations of functional connec-tivity in network models have been reported [2]. A diffi-culty for such analytical studies is that they require in principle characterizing the bifurcation points (i.e. the parameter values at which the network undergoes a sud-den change in dynamics) and how functional connectivity changes close to such points. Given that biological net-works have a finite number of neurons, it is also impor-tant to develop such analytical studies without relying only on large network approximations that neglect finite-