Bursting synchronization in neuronal assemblies of scale-free networks

•We proposed a mathematical model based on Rulkov map to built a network of networks model for coupled bursting neurons.•We use scale-free networks for the cortical areas and a human connectivity matrix for the connections among the cortical areas.•It is possible to suppress bursting synchronization in the network by applying an external time-delayed feedback signal. We investigate the synchronization properties of a neuronal network model inspired on the connection architecture of the human cerebral cortex. The neuronal model is composed of an assembly of networks, where each one of them is a scale-free network and the connections between them are taken from a human connectivity matrix proposed by Lo and collaborators [J. Neuroscience 30, 16876 (2010)]. The neuronal dynamics is governed by the Rulkov two-dimensional discrete-time map and the coupling between neurons and the different cortical regions occurs by means of chemical synapses. Individual neurons display bursting activity with characteristic phases and frequencies. Bursting synchronization is achieved for certain values of the chemical coupling strength in the network model and can be related to the presence of some pathological rhythms. The total or partial suppression of bursting synchronization has been pointed as a dynamical mechanism underlying deep brain stimulation techniques to mitigate such pathologies. In this work a synchronization suppression technique is employed through the application of an external signal based on the time-delayed mean field in certain areas of the neuronal network. Our results show that the suppression of synchronization depends on the values of the time delay and intensity of the applied signal.