The role of the fitness model in the suppression of neuronal synchronous behavior with three-stage switching control in clustered networks

In this work, we investigate the synchronization of neuronal activity through a model of a clustered network formed by scale-free subnetworks. These simulate the areas of the cerebral cortex and capture the spatial distribution of the vertices. The growth of the scale-free subnetworks takes place according to the fitness model, and the architecture of the clustered network presents internal and external links to simulate connections inside and between cortical areas. The corticocortical connections are established according to a human connectivity matrix obtained through experimental data. The model also considers electrical and chemical synapses. A two-dimensional map, in the bursting regime, simulates the dynamic behavior of the neuron. The high synchronization of neuronal activity is revealed by the Kuramoto order parameter. To corroborate the analyses using the order parameter, we calculate a suppression measure. In order to suppress this synchronization, we propose a three-stage switching control as a function of the delayed mean-field in each subnetwork. This suppressor agent is effective in two scenarios, whether applied according to the spatial distribution of neurons or in the emitting hubs of the subnetworks. Our results show that the fitness model has a relevant role in the study of neuronal activity suppression, allied to the application of a three-stage switching control by means of a time-delayed feedback method being an efficient way to suppress synchronization in clustered networks. •We simulate cortical areas according to the fitness model to investigate the influence of hubs in the suppression of network synchronization.•The cortical areas are interconnected forming a clustered network to show emerging synchronization effects in the cerebral cortex.•We apply a synchronization suppressor agent acting like a three-stage switching to the network.•Our results have shown that the graph topology used to simulate the cortical areas play an important role in suppressing synchronization.