FitzHugh-Nagumo equations with generalized diffusive coupling
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 defin...
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AIMS Press
2013-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.203 |
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| author | Anna Cattani |
| author_facet | Anna Cattani |
| author_sort | Anna Cattani |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-64023e02d25b4b0cb74f034d82e0e053 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-64023e02d25b4b0cb74f034d82e0e0532025-01-24T02:28:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-09-0111220321510.3934/mbe.2014.11.203FitzHugh-Nagumo equations with generalized diffusive couplingAnna Cattani0Department of Mathematical Sciences, Corso Duca degli Abruzzi 24, 10129 TorinoThe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.203stability analysisfitzhugh-nagumo modelbiological neural networktravelling pulses.diffusive coupling |
| spellingShingle | Anna Cattani FitzHugh-Nagumo equations with generalized diffusive coupling Mathematical Biosciences and Engineering stability analysis fitzhugh-nagumo model biological neural network travelling pulses. diffusive coupling |
| title | FitzHugh-Nagumo equations with generalized diffusive coupling |
| title_full | FitzHugh-Nagumo equations with generalized diffusive coupling |
| title_fullStr | FitzHugh-Nagumo equations with generalized diffusive coupling |
| title_full_unstemmed | FitzHugh-Nagumo equations with generalized diffusive coupling |
| title_short | FitzHugh-Nagumo equations with generalized diffusive coupling |
| title_sort | fitzhugh nagumo equations with generalized diffusive coupling |
| topic | stability analysis fitzhugh-nagumo model biological neural network travelling pulses. diffusive coupling |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.203 |
| work_keys_str_mv | AT annacattani fitzhughnagumoequationswithgeneralizeddiffusivecoupling |