Effects of feedback control in small-world neuronal networks interconnected according to a human connectivity map

Abstract

In this work, we consider a phenomenological two-dimensional discrete model coupled in a structure of a clustered network to investigate the suppression of neuronal synchronization in a complex network. We constructed a network according to a weighted human connectivity matrix and an adjacency matrix that carries small-world properties. The coupling between neurons is inserted through a chemical synapse term and a neuronal activation function. The neuronal synchronization is measured by the Kuramoto order parameter. We intend to achieve the suppression of burst phase synchronization, and for that, we use a mathematical tool, based on the technique of deep brain stimulation, which consists of applying an external signal to the network after a certain time, causing the bursts to desynchronize. Our results are efficient when applying the feedback method both in the global network and in the cortical regions. We have seen that for cortical regions, synchronization is more difficult to suppress, however, by slightly increasing the perturbation, we are able to achieve the desired effect. This shows that it is possible to use the control efficiently in isolated cortical areas, therefore, we present a new alternative to conventional methods, avoiding to apply the control to the entire network to obtain the same results.