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Uspekhi Mat. Nauk, 2012, Volume 67, Issue 2(404), Pages 109–156 (Mi umn9469)  

This article is cited in 3 scientific papers (total in 3 papers)

Self-excited wave processes in chains of diffusion-linked delay equations

A. Yu. Kolesova, N. Kh. Rozovb

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

Abstract: A new mathematical object is introduced, a scalar non-linear difference-differential equation with time delay which is a certain modification of the Hutchinson equation well-known in ecology. It is shown that the buffering phenomenon occurs in a one-dimensional chain of diffusion-linked equations of this type. Namely, as the number of links grows in a way compatible with a decrease of the diffusion coefficient, the number of co-existing stable periodic solutions of the system increases without limit.
Bibliography: 15 titles.

Keywords: modified Hutchinson equation, self-excited wave processes, relaxation cycle, asymptotic behaviour, stability.

DOI: https://doi.org/10.4213/rm9469

Full text: PDF file (979 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2012, 67:2, 297–343

Bibliographic databases:

UDC: 517.926
MSC: Primary 34C26, 92D40; Secondary 34D45, 37N25
Received: 14.06.2011

Citation: A. Yu. Kolesov, N. Kh. Rozov, “Self-excited wave processes in chains of diffusion-linked delay equations”, Uspekhi Mat. Nauk, 67:2(404) (2012), 109–156; Russian Math. Surveys, 67:2 (2012), 297–343

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
  • Успехи математических наук Russian Mathematical Surveys
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