FitzHugh-Nagumo equations with generalized diffusive coupling

  • Received: 01 September 2012 Accepted: 29 June 2018 Published: 01 October 2013
  • MSC : Primary: 92C42; Secondary: 68R10.

  • The aim of this work is to investigate the dynamics of a neural network, in which neurons, individually described by the FitzHugh-Nagumo model, are coupled by a generalized diffusive term. The formulation we are going to exploit is based on the general framework of graph theory.With the aim of defining the connection structure among the excitable elements, the discrete Laplacian matrix plays a fundamental role. In fact, it allows us to model the instantaneous propagation of signals between neurons, which need not be physically close to each other.
        This approach enables us to address three fundamental issues. Firstly, each neuron is described using the well-known FitzHugh-Nagumo model which might allow to differentiate their individual behaviour. Furthermore, exploiting the Laplacian matrix, a well defined connection structure is formalized. Finally, random networks and an ensemble of excitatory and inhibitory synapses are considered.
        Several simulations are performed to graphically present how dynamics within a network evolve. Thanks to an appropriate initial stimulus a wave is created: it propagates in a self-sustained way through the whole set of neurons. A novel graphical representation of the dynamics is shown.

    Citation: Anna Cattani. FitzHugh-Nagumo equations with generalized diffusive coupling[J]. Mathematical Biosciences and Engineering, 2014, 11(2): 203-215. doi: 10.3934/mbe.2014.11.203

    Related Papers:

  • The aim of this work is to investigate the dynamics of a neural network, in which neurons, individually described by the FitzHugh-Nagumo model, are coupled by a generalized diffusive term. The formulation we are going to exploit is based on the general framework of graph theory.With the aim of defining the connection structure among the excitable elements, the discrete Laplacian matrix plays a fundamental role. In fact, it allows us to model the instantaneous propagation of signals between neurons, which need not be physically close to each other.
        This approach enables us to address three fundamental issues. Firstly, each neuron is described using the well-known FitzHugh-Nagumo model which might allow to differentiate their individual behaviour. Furthermore, exploiting the Laplacian matrix, a well defined connection structure is formalized. Finally, random networks and an ensemble of excitatory and inhibitory synapses are considered.
        Several simulations are performed to graphically present how dynamics within a network evolve. Thanks to an appropriate initial stimulus a wave is created: it propagates in a self-sustained way through the whole set of neurons. A novel graphical representation of the dynamics is shown.


    加载中
    [1] Linear Algebra Appl., 436 (2012), 99-111.
    [2] Phys. Rev. E (3), 436 (2012), 99-111.
    [3] Ph.D thesis, Politecnico di Torino, ongoing.
    [4] Biophysical Journal, 1 (1961), 445-466.
    [5] J. Physiol., 117 (1952), 500-544.
    [6] third edition, Springer-Verlag, New York, 2002.
    [7] Progress of Theoretical Physics Supplements, 161 (2006), 389-392.
    [8] Review of Modern Physics, 47 (1975), 487-533.
  • Reader Comments
  • © 2014 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1944) PDF downloads(620) Cited by(9)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog