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@article{INTO_2019_173_a2, author = {V. E. Goryunov and M. M. Preobrazhenskaya}, title = {Quasi-stability of coexisting attractors of a neurodynamic model with delay}, journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory}, pages = {26--47}, publisher = {mathdoc}, volume = {173}, year = {2019}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/INTO_2019_173_a2/} }
TY - JOUR AU - V. E. Goryunov AU - M. M. Preobrazhenskaya TI - Quasi-stability of coexisting attractors of a neurodynamic model with delay JO - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory PY - 2019 SP - 26 EP - 47 VL - 173 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/INTO_2019_173_a2/ LA - ru ID - INTO_2019_173_a2 ER -
%0 Journal Article %A V. E. Goryunov %A M. M. Preobrazhenskaya %T Quasi-stability of coexisting attractors of a neurodynamic model with delay %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2019 %P 26-47 %V 173 %I mathdoc %U http://geodesic.mathdoc.fr/item/INTO_2019_173_a2/ %G ru %F INTO_2019_173_a2
V. E. Goryunov; M. M. Preobrazhenskaya. Quasi-stability of coexisting attractors of a neurodynamic model with delay. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 26-47. http://geodesic.mathdoc.fr/item/INTO_2019_173_a2/
[1] Aleshin S. V., “Otsenka invariantnykh chislovykh pokazatelei attraktorov sistem differentsialnykh uravnenii s zapazdyvaniem”, Vychislitelnye tekhnologii v estestvennykh naukakh, Nauch. konf. «Metody superkompyuternogo modelirovaniya» (Tarusa, 1–3 oktyabrya 2014), eds. Nazirov R. R., Schur L. N., In-t kosmich. issled. RAN, M., 2014, 10–17
[2] Bylov B. F., Vinograd R. E., Grobman D. M., Nemytskii V. V., Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti, Nauka, M., 1966
[3] Glyzin S. D., Kolesov A. Yu., Marushkina E. A., Preobrazhenskaya M. M., “Relaksatsionnye avtokolebaniya v sisteme iz dvukh sinapticheski svyazannykh impulsnykh neironov”, XIX Mezhdunar. nauch.-tekhn. konferentsiya «Neiroinformatika–2017» (Moskva, 2-6 oktyabrya 2017), v. 1, M., 2017, 29–39
[4] Glyzin S. D., Kolesov A. Yu, Rozov N. Kh., “Diskretnye avtovolny v neironnykh sistemakh”, Zh. vychisl. mat. mat. fiz., 52:5 (2012), 840–858 | MR | Zbl
[5] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Ob odnom sposobe matematicheskogo modelirovaniya khimicheskikh sinapsov”, Differ. uravn., 49:10 (2013), 1227–1244 | MR | Zbl
[6] Glyzin S. D., Kolesov A. Yu, Rozov N. Kh., “Relaksatsionnye avtokolebaniya v setyakh Khopfilda s zapazdyvaniem”, Izv. RAN. Ser. mat., 77:2 (2013), 53–96 | DOI | MR | Zbl
[7] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Modelirovanie effekta vzryva v neironnykh sistemakh”, Mat. zametki., 93:5 (2013), 684–701 | DOI | MR | Zbl
[8] Glyzin S. D., Kolesov A. Yu, Rozov N. Kh., “Relaksatsionnye avtokolebaniya v setyakh impulsnykh neironov”, Usp. mat. nauk., 70:3 (423) (2015), 3–76 | DOI | MR | Zbl
[9] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Kvaziustoichivye struktury v koltsevykh gennykh setyakh”, Zh. vychisl. mat. mat. fiz., 58:5 (2018), 682–704 | DOI
[10] Kaschenko S. A., Maiorov V. V., Modeli volnovoi pamyati, Librokom, M., 2009
[11] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., “Rele s zapazdyvaniem i ego $C^1$-approksimatsiya”, Tr. Mat. in-ta im. V. A. Steklova RAN, 216, 1997, 126–153 | Zbl
[12] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., “Ob odnoi modifikatsii uravneniya Khatchinsona”, Zh. vychisl. mat. mat. fiz., 50:12 (2010), 2099–2112 | MR | Zbl
[13] Oseledets V. I., “Multiplikativnaya ergodicheskaya teorema. Kharakteristicheskie pokazateli Lyapunova dinamicheskikh sistem”, Tr. Mosk. mat. o-va, 19, 1968, 179–210 | Zbl
[14] Preobrazhenskaya M. M., “Relaksatsionnye tsikly v modeli sinapticheski vzaimodeistvuyuschikh ostsillyatorov”, Model. anal. inform. sistem., 24:2 (2017), 186–204 | MR
[15] Preobrazhenskaya M. M., “Impulsno-refrakternyi rezhim v koltsevoi tsepi sinapticheski svyazannykh ostsillyatorov neironnogo tipa”, Model. anal. inform. sistem., 24:5 (2017), 550–566 | MR
[16] Cheney W., Kincaid D., Linear Algebra: Theory and Applications, Jones and Bartlett, Sudbury, Massachusetts, 2012 | Zbl
[17] Hairer E., Wanner G., Norsett S. P., Solving Ordinary Differential Equations, v. I, Nonstiff Problems, Springer-Verlag, Berlin–Heidelberg, 2008 | MR
[18] Preobrazhenskaya M. M., “Multipliers of an antiphase solution in a system of two coupled nonlinear relaxation oscillators”, J. Phys. Conf. Ser., 1163 (2019), 012062 | DOI
[19] Rabinovich M. I., Varona P., Selverston A. I., Abarbanel H. D. I., “Dynamical principles in neuroscience”, Rev. Mod. Phys., 78 (2006), 1213–1265 | DOI
[20] Somers D., Kopell N., “Rapid synchronization through fast threshold modulation”, Biol. Cybern., 68 (1993), 393–407 | DOI
[21] Somers D., Kopell N., “Anti-phase solutions in relaxation oscillators coupled through excitatory interactions”, J. Math. Biol., 33 (1995), 261–280 | MR | Zbl
[22] Wolf A., Swift J. B., Swinney H. L., Vastano J. A., “Determining Lyapunov exponents from a time series”, Phys. D., 16 (1985), 285–317 | DOI | MR | Zbl