Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons

unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The formation of oscillating phase clusters in a network of identical Hodgkin–Huxley neurons is studied, along with their dynamic behavior. The neu-rons are synaptically coupled in an all-to-all manner, yet the synaptic coupling char-acteristic time is heterogeneous across the connections. In a network of N neurons where this heterogeneity is characterized by a prescribed random variable, the oscil-latory single-cluster state can transition—through N − 1 (possibly perturbed) period-doubling and subsequent bifurcations—to a variety of multiple-cluster states. The clustering dynamic behavior is computationally studied both at the detailed and the coarse-grained levels, and a numerical approach that can enable studying the coarse-grained dynamics in a network of arbitrarily large size is suggested. Among a number of cluster states formed, double clusters, composed of nearly equal sub-network sizes are seen to be stable; interestingly, the heterogeneity parameter in each of the double-cluster components tends to be consistent with the random variable over the entir