Emergent Dynamics of Neuronal Networks with Differing Time-scales and Modular Structure

Abstract

The dynamics of the mammalian brain is captured using nonlinear dynamics in the framework of complex networks. We study the dynamics of Hindmarsh- Rose neurons with time-scale mismatch in detail, for both simplistic and realistic network models and develop various schemes for characterizing the collective dynamics of the neurons. For a simple system with two mutually coupled neurons with di ering time-scales, we observe that the di erence in timescales leads to synchronized states of frequency suppression. In a ring of HR neurons, with time-scales decreasing sequentially, we nd the neurons go into Synchronized Frequency Suppressed Clusters. We extend our model to more realisitic models of neuronal networks like modular networks. Modular networks of HR neurons show various interesting dynamical states like de-synchronized states, phase synchronization and activity death states. Further characterization of frequency suppressed states in such networks can lead to better understanding of coding of information in neuronal networks.