Open AccessAsymmetric Interaction of a Pair FitzHugh–Nagumo Oscillators
Author(s) -
Елена Александровна Марушкина
Publication year - 2015
Publication title -
modelirovanie i analiz informacionnyh sistem
Language(s) - English
Resource type - Journals
eISSN - 2313-5417
pISSN - 1818-1015
DOI - 10.18255/1818-1015-2014-1-115-120
Subject(s) - eigenvalues and eigenvectors , diffusion , mathematics , physics , mathematical analysis , matrix (chemical analysis) , statistical physics , classical mechanics , quantum mechanics , chemistry , chromatography
A pair of diffusion connected FitzHugh–Nagumo oscillators with an asymmetric interaction are considered. The problem is investigated in the close to critical case, where the matrix of the linear part of the system has a pair of purely imaginary eigenvalues. The normal form is constructed and its coefficients are determined depending on the initial parameters. The source system may be in two different situations: stable singlefrequency oscillations with two different frequencies coexist or a single-frequency mode branches from the equilibrium. The obtained asymptotic results are supplemented by the numerical analysis.