Bursting synchronization in scale-free networks

Neuronal networks in some areas of the brain cortex present the scale-free property, i.e., the neuron connectivity is distributed according to a power-law, such that neurons are more likely to couple with other already well-connected ones. Neuron activity presents two timescales, a fast one related to action-potential spiking, and a slow timescale in which bursting takes place. Some pathological conditions are related with the synchronization of the bursting activity in a weak sense, meaning the adjustment of the bursting phase due to coupling. Hence it has been proposed that an externally applied time-periodic signal be applied in order to control undesirable synchronized bursting rhythms. We investigated this kind of intervention using a two-dimensional map to describe neurons with spiking– bursting activity in a scale-free network.