Delay-induced locking in bursting neuronal networks.

In this paper, the collective behaviors for ring structured bursting neuronal networks with electrical couplings and distance-dependent delays are studied. Each neuron is modeled by the Hindmarsh-Rose neuron. Through changing time delays between connected neurons, different spatiotemporal patterns are obtained. These patterns can be explained by calculating the ratios between the bursting period and the delay which exhibit clear locking relations. The holding and the failure of the lockings are investigated via bifurcation analysis. In particular, the bursting death phenomenon is observed for large coupling strengths and small time delays which is in fact the result of the partial amplitude death in the fast subsystem. These results indicate that the collective behaviors of bursting neurons critically depend on the bifurcation structure of individual ones and thus the variety of bifurcation types for bursting neurons may create diverse behaviors in similar neuronal ensembles.