Propagation of Excitations in Clusterized Nets near Critical Point

In this master's thesis the peculiar properties of propagation of excitations in a network with seven clusters are studied. The study of propagation of excitation in highly structured networks is of great interest, for the reason that many real network systems are clustered. Clusterized network was created from the the Erdos-Renyi network using the algorithm of directed evolution with preservation of the nodes' degree. In the course of the work execution, a specific software was written in Python. Using the software, the trajectories of changes of the number of active nodes in time were generated for the whole network, as well as for individual clusters. The simulation allowed revealing the existence of three modes of propagation of excitations: the blanking mode, the mode of unstable combustion and the mode of stable combustion. Specifically, the synchronization of activity between clusters were studied. It was found that in the seven-cluster network the appearance of cluster-cluster correlated activity modes depends on individual pair of clusters, unlike the Erdos-Renyi network.