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From Net Topology to Synchronization in HR Neuron Grids

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  • 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.
    Mathematics Subject Classification: 92C29.


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