2005, 2(1): 53-77. doi: 10.3934/mbe.2005.2.53

From Net Topology to Synchronization in HR Neuron Grids

1. 

DIEES, University of Catania, Viale Andrea Doria 6, 95123, Catania, Italy, Italy, Italy, Italy, Italy, Italy

2. 

PST Group, Corporate R&D, STMicroelectronics, Catania site, Stradale Primosole 50, 95121 Catania, Italy

Received  June 2004 Revised  August 2004 Published  November 2004

In this paper, we investigate the role of topology on synchronization, a fundamental feature of many technological and biological fields. We study it in Hindmarsh-Rose neural networks, with electrical and chemical synapses, where neurons are placed on a bi-dimensional lattice, folded on a torus, and the synapses are set according to several topologies. In addition to the standard topologies used in other studies, we introduce a new model that generalizes the Barabási-Albert scale-free model, taking into account the physical distance between nodes. Such a model, because of its plausibility both in the static characteristics and in the dynamical evolution, is a good representation for those real networks (such as a network of neurons) whose edges are not costless. We investigate synchronization in several topologies; the results strongly depend on the adopted synapse model.
Citation: Stefano Cosenza, Paolo Crucitti, Luigi Fortuna, Mattia Frasca, Manuela La Rosa, Cecilia Stagni, Lisa Usai. From Net Topology to Synchronization in HR Neuron Grids. Mathematical Biosciences & Engineering, 2005, 2 (1) : 53-77. doi: 10.3934/mbe.2005.2.53
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