From Net Topology to Synchronization in HR Neuron Grids
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1.
DIEES, University of Catania, Viale Andrea Doria 6, 95123, Catania
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2.
PST Group, Corporate R&D, STMicroelectronics, Catania site, Stradale Primosole 50, 95121 Catania
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Received:
01 June 2004
Accepted:
29 June 2018
Published:
01 November 2004
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MSC :
92C29.
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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.
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[J]. Mathematical Biosciences and Engineering, 2005, 2(1): 53-77. doi: 10.3934/mbe.2005.2.53
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Abstract
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.
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