ISSN 0869-6632 (Print)
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Dmitrichev A. S., Nekorkin V. I. Stationary localized activity structures in two-dimensional ensemble of Fitzhugh–Nagumo neurons with oscillatory threshold. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 3, pp. 71-87. DOI: 10.18500/0869-6632-2008-16-3-71-87

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Stationary localized activity structures in two-dimensional ensemble of Fitzhugh–Nagumo neurons with oscillatory threshold

Dmitrichev Aleksej Sergeevich, Institute of Applied Physics of the Russian Academy of Sciences
Nekorkin Vladimir Isaakovich, Institute of Applied Physics of the Russian Academy of Sciences

We present the analysis of spatiotemporal dynamics of two-dimensional ensemble of electrically coupled FitzHugh–Nagumo neurons with oscillatory threshold. We show that in this system spatially localized activity structures can be formed. Such structures propagate through the system without changing their shape and velocity. We demonstrate that there exist two types of the structures: single and bound states. General characteristics of localized structures such as regions of existence, geometrical sizes and velocity are investigated. We also study structures interaction and give explanation for their existence and stability in terms of trajectories in associating with the ensemble multidimensional phase space.

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