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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 4, Pages 73–108 (Mi izv8102)  

This article is cited in 11 scientific papers (total in 11 papers)

The buffer phenomenon in ring-like chains of unidirectionally connected generators

S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University

Abstract: We introduce a new object, namely, a system of ordinary differential equations which is a mathematical model of a ring-like chain of unidirectionally connected RCL-generators. To study periodic solutions of travelling wave type of this system, some special tricks are used which reduce the existence and stability problems for cycles to the investigation of auxiliary delay equations. Using this approach, we establish that the number of stable travelling waves simultaneously existing in the chain increases unboundedly as the number of links of the chain increases, that is, the well-known buffer phenomenon occurs.

Keywords: chain of unidirectionally connected generators, travelling wave, asymptotic behaviour, stability, buffer phenomenon.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00384_а
12-01-00155_а


DOI: https://doi.org/10.4213/im8102

Full text: PDF file (778 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2014, 78:4, 708–743

Bibliographic databases:

UDC: 517.926
MSC: Primary 34C05; Secondary 34C25, 34C26
Received: 12.02.2013
Revised: 21.07.2013

Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “The buffer phenomenon in ring-like chains of unidirectionally connected generators”, Izv. RAN. Ser. Mat., 78:4 (2014), 73–108; Izv. Math., 78:4 (2014), 708–743

Citation in format AMSBIB
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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. 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
    2. 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
    3. 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
    4. V. P. Golubyatnikov, N. E. Kirillova, “O tsiklakh v modelyakh funktsionirovaniya koltsevykh gennykh setei”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 54–63  mathnet  crossref
    5. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Stable relaxation cycle in a bilocal neuron model”, Differ. Equ., 54:10 (2018), 1285–1309  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    6. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Quasi-stable structures in circular gene networks”, Comput. Math. Math. Phys., 58:5 (2018), 659–679  mathnet  crossref  crossref  isi  elib
    7. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “A self-symmetric cycle in a system of two diffusely connected Hutchinson's equations”, Sb. Math., 210:2 (2019), 184–233  mathnet  crossref  crossref  adsnasa  isi  elib
    8. A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “On a Mathematical Model of Biological Self-Organization”, Proc. Steklov Inst. Math., 304 (2019), 160–189  mathnet  crossref  crossref  isi  elib
    9. Glyzin S.D., Kolesov A.Yu., Rozov N.Kh., International Conference on Computer Simulation in Physics and Beyond, Journal of Physics Conference Series, 1163, ed. Shchur L., IOP Publishing Ltd, 2019  crossref  isi
    10. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Novyi podkhod k modelirovaniyu gennykh setei”, Model. i analiz inform. sistem, 26:3 (2019), 365–404  mathnet  crossref
    11. Glyzin S.D., Kolesov A.Yu., Rozov N.Kh., Vii International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 1205, IOP Publishing Ltd, 2019  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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