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Tr. Mat. Inst. Steklova, 1997, Volume 216, Pages 126–153 (Mi tm1002)  

This article is cited in 25 scientific papers (total in 26 papers)

Relay with delay and its $C^1$-approximation

A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov


Full text: PDF file (2527 kB)

English version:
Proceedings of the Steklov Institute of Mathematics, 1997, 216, 119–146

Bibliographic databases:
UDC: 517.929
Received in December 1996

Citation: A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Relay with delay and its $C^1$-approximation”, Dynamical systems and related topics, Collection of articles. To the 60th anniversary of academician Dmitrii Viktorovich Anosov, Tr. Mat. Inst. Steklova, 216, Nauka, Moscow, 1997, 126–153; Proc. Steklov Inst. Math., 216 (1997), 119–146

Citation in format AMSBIB
\Bibitem{KolMisRoz97}
\by A.~Yu.~Kolesov, E.~F.~Mishchenko, N.~Kh.~Rozov
\paper Relay with delay and its $C^1$-approximation
\inbook Dynamical systems and related topics
\bookinfo Collection of articles. To the 60th anniversary of academician Dmitrii Viktorovich Anosov
\serial Tr. Mat. Inst. Steklova
\yr 1997
\vol 216
\pages 126--153
\publ Nauka
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm1002}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1632133}
\zmath{https://zbmath.org/?q=an:0916.34057}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1997
\vol 216
\pages 119--146


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “A modification of Hutchinson's equation”, Comput. Math. Math. Phys., 50:12 (2010), 1990–2002  mathnet  crossref  adsnasa
    2. S. D. Glyzin, “Relaksatsionnye kolebaniya elektricheski svyazannykh neiropodobnykh ostsillyatorov s zapazdyvaniem”, Model. i analiz inform. sistem, 17:2 (2010), 28–47  mathnet  elib
    3. I. V. Paramonov, “Relaksatsionnye tsikly obobschennogo uravneniya impulsnogo neirona”, Model. i analiz inform. sistem, 18:1 (2011), 106–115  mathnet
    4. Glyzin S.D., Kolesov A.Yu., Rozov N.Kh., “Relaxation Self-Oscillations in Neuron Systems: I”, Differ Equ, 47:7 (2011), 927–941  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. D. V. Anosov, S. M. Aseev, R. V. Gamkrelidze, S. P. Konovalov, M. S. Nikol'skii, N. Kh. Rozov, “Evgenii Frolovich Mishchenko (on the 90th anniversary of his birth)”, Russian Math. Surveys, 67:2 (2012), 385–402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. A. Yu. Kolesov, N. Kh. Rozov, “Self-excited wave processes in chains of diffusion-linked delay equations”, Russian Math. Surveys, 67:2 (2012), 297–343  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. A. Yu. Kolesov, N. Kh. Rozov, “Discrete autowaves in systems of delay differential–difference equations in ecology”, Proc. Steklov Inst. Math., 277 (2012), 94–136  mathnet  crossref  mathscinet  isi  elib  elib
    8. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Discrete autowaves in neural systems”, Comput. Math. Math. Phys., 52:5 (2012), 702–719  mathnet  crossref  mathscinet  isi  elib  elib
    9. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Relaxation self-oscillations in Hopfield networks with delay”, Izv. Math., 77:2 (2013), 271–312  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Modeling the Bursting Effect in Neuron Systems”, Math. Notes, 93:5 (2013), 676–690  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations”, Theoret. and Math. Phys., 175:1 (2013), 499–517  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. S. D. Glyzin, E. A. Marushkina, “Relaksatsionnye tsikly v obobschennoi neironnoi modeli s dvumya zapazdyvaniyami”, Model. i analiz inform. sistem, 20:6 (2013), 179–199  mathnet
    13. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “The buffer phenomenon in ring-like chains of unidirectionally connected generators”, Izv. Math., 78:4 (2014), 708–743  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. Yu. V. Bogomolov, S. D. Glyzin, A. Yu. Kolesov, “O chisle sosuschestvuyuschikh avtovolnovykh reshenii tsepochki diffuzionno svyazannykh ostsillyatorov neironnogo tipa”, Model. i analiz inform. sistem, 21:5 (2014), 162–180  mathnet
    15. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Self-excited relaxation oscillations in networks of impulse neurons”, Russian Math. Surveys, 70:3 (2015), 383–452  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Avtovolnovye protsessy v koltsevoi neironnoi tsepi s odnonapravlennoi svyazyu”, Model. i analiz inform. sistem, 22:3 (2015), 404–419  mathnet  crossref  mathscinet  elib
    17. A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “Periodic solutions of travelling-wave type in circular gene networks”, Izv. Math., 80:3 (2016), 523–548  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Buffering in cyclic gene networks”, Theoret. and Math. Phys., 187:3 (2016), 935–951  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    19. Glyzin S.D. Kolesov A.Yu. Rozov N.Kh., “Self-Sustained Relaxation Oscillations in Time-Delay Neural Systems”, Murphys-Hsfs-2014: 7Th International Workshop on Multi-Rate Processes & Hysteresis (Murphys) & the 2Nd International Workshop on Hysteresis and Slow-Fast Systems (Hsfs), Journal of Physics Conference Series, 727, ed. Klein O. Dimian M. Gurevich P. Knees D. Rachinskii D. Tikhomirov S., IOP Publishing Ltd, 2016, UNSP 012004  crossref  isi  scopus  scopus
    20. Glyzin S.D., Kolesov A.Yu., Rozov N.Kh., “Periodic two-cluster synchronization modes in completely connected genetic networks”, Differ. Equ., 52:2 (2016), 157–176  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    21. S. D. Glyzin, A. Yu. Kolesov, E. A. Marushkina, “Relaksatsionnye avtokolebaniya v sisteme iz dvukh sinapticheski svyazannykh impulsnykh neironov”, Model. i analiz inform. sistem, 24:1 (2017), 82–93  mathnet  crossref  mathscinet  elib
    22. M. M. Preobrazhenskaya, “Relaksatsionnye tsikly v modeli sinapticheski vzaimodeistvuyuschikh ostsillyatorov”, Model. i analiz inform. sistem, 24:2 (2017), 186–204  mathnet  crossref  elib
    23. M. M. Preobrazhenskaya, “Impulsno-refrakternyi rezhim v koltsevoi tsepi sinapticheski svyazannykh ostsillyatorov neironnogo tipa”, Model. i analiz inform. sistem, 24:5 (2017), 550–566  mathnet  crossref  elib
    24. Preobrazhenskaia M.M., “The Impulse-Refractive Mode in a Neural Network With Ring Synaptic Interaction”, Autom. Control Comp. Sci., 52:7 (2018), 777–789  crossref  isi  scopus
    25. V. E. Goryunov, M. M. Preobrazhenskaya, “Kvaziustoichivost sosuschestvuyuschikh attraktorov neirodinamicheskoi modeli s zapazdyvaniem”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g. Chast 4, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 173, VINITI RAN, M., 2019, 26–47  mathnet  crossref
    26. M. M. Preobrazhenskaya, “A relay Mackey–Glass model with two delays”, Theoret. and Math. Phys., 203:1 (2020), 524–534  mathnet  crossref  crossref  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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