Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos - Publikacja - MOST Wiedzy

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Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos

Abstrakt

In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical systems with resets, such structures are complex to analyze. In the present context, we use the fact that bursting patterns correspond to periodic orbits of the adaptation map that governs the sequence of values of the adaptation variable at the resets. Using a slow-fast approach, we show that this map converges towards a piecewise linear discontinuous map whose orbits are exactly characterized. That map shows a period-incrementing structure with instantaneous transitions. We show that the period-incrementing structure persists for the full system with non-constant adaptation, but the transitions are more complex. We investigate the presence of chaos at the transitions.

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Informacje szczegółowe

Kategoria:
Publikacja w czasopiśmie
Typ:
artykuł w czasopiśmie wyróżnionym w JCR
Opublikowano w:
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B nr 22, wydanie 10, strony 3967 - 4002,
ISSN: 1531-3492
Język:
angielski
Rok wydania:
2017
Opis bibliograficzny:
Rubin J., Signerska-Rynkowska J., Touboul J., Vidal A.: Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos// DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B. -Vol. 22, iss. 10 (2017), s.3967-4002
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.3934/dcdsb.2017204
Weryfikacja:
Politechnika Gdańska

wyświetlono 19 razy

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