Geodesic
Modeling spike-wave discharges in the brain with small neurooscillator networks
Matematičeskaâ biologiâ i bioinformatika, Tome 15 (2020) no. 2, pp. 138-147.

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Pathology of coupling architecture in the thalamo-cortical system is considered to be the main cause of absence epilepsy, which eletroencephalographic primary manifestation is spike-wave discharges. The onset of discharge may be An increase of intracortical connectivity or external stimulation of the cortex or thalamus can be an immediate trigger for discharge onset. At the same time, the mechanisms of discharge termination are still not clear; so from the point of view of the dynamical system theory, the spike-wave discharge can be considered as a long transient process. In this paper, we propose a simple mathematical model of 14 identical Fitzhugh–Nagumo neurons, organized in accordance with modern ideas about the thalamo-cortical brain network. In this model long transients in response to short-term pulse driving from a separate neuron, representing the nervus trigeminus, are shown to be possible. Bifurcation analysis reveals such transients to develop in the system in the vicinity of the bifurcation of the cycle birth from the condensation of phase trajectories. The model should be useful as part of more detailed models of the thalamo-cortical system created for fundamental purposes, as well as it can be used to test the effects of electrical brain stimulation, pharmacological effects, and to test methods for evaluating connectivity in the brain. 
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     title = {Modeling spike-wave discharges in the brain with small neurooscillator networks},
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A. A. Kapustnikov; M. V. Sysoeva; I. V. Sysoev. Modeling spike-wave discharges in the brain with small neurooscillator networks. Matematičeskaâ biologiâ i bioinformatika, Tome 15 (2020) no. 2, pp. 138-147. http://geodesic.mathdoc.fr/item/MBB_2020_15_2_a9/

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