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Ultima descărcare din IBN: 2023-10-02 09:46 |
SM ISO690:2012 GEORGESCU, Adelina, NISTOR, Gheorghe, POPESCU, Marin-Nicolae, POPA, Dinel. A closed form asymptotic solution for the FitzHugh-Nagumo model. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2008, nr. 2(57), pp. 24-34. ISSN 1024-7696. |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
Numărul 2(57) / 2008 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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Pag. 24-34 | ||||||
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By means of a change of unknown function and independent variable, the Cauchy problem of singular perturbation from electrophysiology, known as the FitzHugh-Nagumo model, is reduced to a regular perturbation problem (Section 1). Then, by applying the regular perturbation technique to the last problem and using an existence, uniqueness and asymptotic behavior theorem of the second and third
author, the models of asymptotic approximation of an arbitrary order are deduced
(Section 2). The closed-form expressions for the solution of the model of first order
asymptotic approximation and for the time along the phase trajectories are derived
in Section 3. In Section 4, by applying several times the method of variation of
coefficients and prime integrals, the closed-form solution of the model of second order
asymptotic approximation is found. The results from this paper served to the author
to study (elsewhere) the relaxation oscillations versus the oscillations in two and three times corresponding to concave limit cycles (canards). |
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Cuvinte-cheie Asymptotic solution, FitzHugh-Nagumo model, electrophysiology., singular perturbation |
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