Geodesic
Modeling the Bursting Effect in Neuron Systems
Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 684-701

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We propose a new method for modeling the well-known phenomenon of “bursting behavior” in neuron systems by invoking delay equations. Namely, we consider a singularly perturbed nonlinear difference-differential equation with two delays describing the functioning of an isolated neuron. Under a suitable choice of parameters, we establish the existence of a stable periodic motion with any prescribed number of spikes on a closed time interval equal to the period length.
Keywords: “bursting behavior” in neuron systems, difference-differential equation, relay equation, Cauchy problem, Schauder principle, relaxation cycle, spiking, stability. 
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     author = {S. D. Glyzin and A. Yu. Kolesov and N. Kh. Rozov},
     title = {Modeling the {Bursting} {Effect} in {Neuron} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a3/}
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S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Modeling the Bursting Effect in Neuron Systems. Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 684-701. http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a3/