Frequency locking and travelling burst sequences in community structured network of inhibitory neurons with differing time-scales

Abstract: We report the emergent dynamics of a community structured modular network of chaotic Hindmarsh-Rose (HR) neurons with inhibitory synapses. We find the inhibitory coupling between the neuronal modules lead to complete synchronization of neurons in a module, and also pushes modules into interesting sequences of travelling burst patterns. When dynamical time-scales vary for neurons in different modules, hence breaking the symmetry among them, we see specific sequences of travelling burst patterns that are characteristic of the time-scale mismatch and coupling strengths. Thus for a modular network with two time-scales, the neuronal communities enter into synchronized frequency locked clusters with the bursting sequences having recurring patterns. Our study provides a complete characterization of the spatio-temporal regularity in terms of frequency locking for temporal order and burst sequence patterns for spatial order in the collective dynamics of the neuronal clusters. Our results have significance in the process of information coding in terms of frequency of firing dynamics among neurons and in selective communication based on the sequences of bursts.