From Net Topology to Synchronization in HR Neuron Grids - Stefano Cosenza; Paolo Crucitti; Luigi Fortuna; Mattia Frasca; Manuela La Rosa; Cecilia Stagni; Lisa Usai (Mathematical Biosciences and Engineering)
In this paper, we investigate the role of topology onsynchronization, a fundamental feature of many technological andbiological fields. We study it in Hindmarsh-Rose neural networks,with electrical and chemical synapses, where neurons are placed ona bi-dimensional lattice, folded on a torus, and the synapses areset according to several topologies. In addition to the standardtopologies used in other studies, we introduce a new model thatgeneralizes the Barabási-Albert scale-free model, taking intoaccount the physical distance between nodes. Such a model, becauseof its plausibility both in the static characteristics and in thedynamical evolution, is a good representation for those realnetworks (such as a network of neurons) whose edges are notcostless. We investigate synchronization in several topologies;the results strongly depend on the adopted synapse model.