Delayed feedback control of bursting synchronization in a scale-free neuronal network

Several neurological diseases (e.g. essential tremor and Parkinson’s disease) are related to pathologically enhanced synchronization of bursting neurons. Suppression of these synchronized rhythms has potential implications in electrical deep-brain stimulation research. We consider a simplified model of a neuronal network where the local dynamics presents a bursting timescale, and the connection architecture displays the scale-free property (power-law distribution of connectivity). The networks exhibit collective oscillations in the form of synchronized bursting rhythms, without affecting the fast timescale dynamics. We investigate the suppression of these synchronized oscillations using a feedback control in the form of a time-delayed signal. We located domains of bursting synchronization suppression in terms of perturbation strength and time delay, and present computational evidence that synchronization suppression is easier in scale-free networks than in the more commonly studied global (mean-field) networks.