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.
