Geodesic
Dynamics of two coupled neuron-type oscillators
Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 2, pp. 75-88 
S. D. Glyzin; E. O. Kiseleva. Dynamics of two coupled neuron-type oscillators. Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 2, pp. 75-88. http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a12/
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     url = {http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Dynamics of two diffusion coupled close oscillators occuring in nerve cells simulation is considered. For close to critical values of problem parameters the normal form for amplitude and phase variables is constructed. Phase reconstructions of the normal form when changing the coupling parameter of the system are analyzed. Numerical analysis of the original system shows correspondence between local phase reconstructions and phase reconstructions of the normal form in a wide area of parameters values.

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

[2] S. A. Kaschenko, V. V. Maiorov, “Ob odnom differentsialno-raznostnom uravnenii, modeliruyuschem impulsnuyu aktivnost neirona”, Matematicheskoe modelirovanie, 5:12 (1993), 13–25 | MR

[3] V. V. Maiorov, I. Yu. Myshkin, “Matematicheskoe modelirovanie neironov seti na osnove uravnenii s zapazdyvaniem”, Matematicheskoe modelirovanie, 2:11 (1990), 64–76 | MR

[4] A. Yu. Kolesov, N. Kh. Rozov, Invariantnye tory nelineinykh volnovykh uravnenii, Fizmatlit, M., 2004

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

[6] S. D. Glyzin, “Statsionarnye rezhimy odnoi konechnoraznostnoi approksimatsii uravneniya Khatchinsona s diffuziei”, Kachestvennye i priblizhennye metody issledovaniya operatornykh uravnenii, Mezhvuz. sb., Yarosl. un-t, Yaroslavl, 1986, 112–127 | MR