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Mathematical Biosciences and Engineering

2005, Volume 2, Issue 1: 53-77. doi: 10.3934/mbe.2005.2.53
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From Net Topology to Synchronization in HR Neuron Grids

  • 1.
    DIEES, University of Catania, Viale Andrea Doria 6, 95123, Catania
  • 2.
    PST Group, Corporate R&D, STMicroelectronics, Catania site, Stradale Primosole 50, 95121 Catania
  • Received: 01 June 2004 Accepted: 29 June 2018 Published: 01 November 2004

  • MSC : 92C29.

  • 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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  • 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.


  • This article has been cited by:

    1. M. S. Baptista, F. M. Moukam Kakmeni, C. Grebogi, Combined effect of chemical and electrical synapses in Hindmarsh-Rose neural networks on synchronization and the rate of information, 2010, 82, 1539-3755, 10.1103/PhysRevE.82.036203
    2. Lin Min, Wang Gang, Chen Tian-Lun, A Modified Earthquake Model Based on Generalized Barabási–Albert Scale-Free Networks, 2006, 46, 0253-6102, 1011, 10.1088/0253-6102/46/6/011
    3. Lin Min, Wang Gang, Chen Tian-Lun, Self-organized Criticality in a Modified Evolution Model on Generalized Barabási–Albert Scale-Free Networks, 2007, 47, 0253-6102, 512, 10.1088/0253-6102/47/3/027
    4. D. R. Paula, A. D. Araújo, J. S. Andrade, H. J. Herrmann, J. A. C. Gallas, Periodic neural activity induced by network complexity, 2006, 74, 1539-3755, 10.1103/PhysRevE.74.017102
    5. Lin Min, Wang Gang, Chen Tian-Lun, Modified DM Models for Aging Networks Based on Neighborhood Connectivity, 2008, 49, 0253-6102, 243, 10.1088/0253-6102/49/1/51
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  • © 2005 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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