Geodesic
The factor of delay in a system of coupled oscillators FitzHugh--Nagumo
Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 3, pp. 134-143.

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The dynamics of two weakly coupled close oscillators FitzHugh–Nagumo occuring in the simulation of the electric impulse exchange between nerve cells is considered. The delay in a connecting element between two oscillators is taken into account. Despite of the weakness of interaction, it is shown by local asymptotic methods that the introduction of a delay leads to significant changes in the script of phase reconstructions. The corresponding numerical analysis allows us to demonstrate that the introduction of the appropriate delay let us avoid the situation of the coexistence of a stable synchronous cycle and nonsynchronous oscillations.
Mots-clés : autooscillations, bifurcations.
Keywords: delay, normal form method 
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S. D. Glyzin; E. A. Soldatova. The factor of delay in a system of coupled oscillators FitzHugh--Nagumo. Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 3, pp. 134-143. http://geodesic.mathdoc.fr/item/MAIS_2010_17_3_a8/

[1] R. FitzHugh, “Threshold and plateaus in the Hodgkin-Huxley nerve equations”, The Journal of Generical Physiology, 43 (1960), 867–896 | DOI

[2] J. Nagumo, S. Arimoto, S. Youshizawa, “An active pulse transmission line simulating nerve axon”, Proc IRE, 50 (1962), 2061–2070 | DOI

[3] A. L. Hodgkin, A. F. Huxley, “A quantitative description of membrane current and application to conduction and excitation in nerve”, Journal Physiol, 117 (1952), 500–544

[4] D. G. Aronson, G. B. Ermentrout, N. Kopell, “Amplitude Response of Coupled Oscillators”, Physica D, 41 (1990), 403–449 | DOI | MR | Zbl

[5] D. Terman, N. Kopell, A. Bose, “Dynamics of two mutually coupled slow inhibitory neurons”, Physica D, 117 (1998), 241–275 | DOI | MR | Zbl

[6] S. D. Glyzin, A. Yu. Kolesov, Lokalnye metody analiza dinamicheskikh sistem: uchebnoe posobie, Yaroslavl, 2006, 92 pp.

[7] S. D. Glyzin, “Stsenarii fazovykh perestroek odnoi konechnoraznostnoi modeli uravneniya “reaktsiya-diffuziya””, Differentsialnye uravneniya, 33:6 (1997), 805–811 | MR | Zbl

[8] S. D. Glyzin, E. O. Kiseleva, “Uchet zapazdyvaniya v tsepochke svyazi mezhdu ostsillyatorami”, Modelirovanie i analiz informatsionnykh sistem, 17:2 (2010), 133–143