RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 Tr. Mat. Inst. Steklova, 2019, Volume 304, Pages 174–204 (Mi tm3966)

On a Mathematical Model of Biological Self-Organization

A. Yu. Kolesova, N. Kh. Rozovb, V. A. Sadovnichiib

a P. G. Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150003 Russia
b Moscow State University, Moscow, 119991 Russia

Abstract: A system of two generalized Hutchinson's equations coupled by linear diffusion terms is considered. It is established that for an appropriate choice of parameters, the system has a stable relaxation cycle whose components turn into each other under a certain phase shift. A number of additional properties of this cycle are presented that allow one to interpret it as a self-organization mode.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-29-10055 This work was supported by the Russian Foundation for Basic Research, project no. 18-29-10055.

DOI: https://doi.org/10.4213/tm3966

Full text: PDF file (352 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 304, 160–189

Bibliographic databases:

UDC: 517.926
Revised: September 14, 2018
Accepted: January 16, 2019

Citation: A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “On a Mathematical Model of Biological Self-Organization”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 174–204; Proc. Steklov Inst. Math., 304 (2019), 160–189

Citation in format AMSBIB
\Bibitem{KolRozSad19} \by A.~Yu.~Kolesov, N.~Kh.~Rozov, V.~A.~Sadovnichii \paper On a Mathematical Model of Biological Self-Organization \inbook Optimal control and differential equations \bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin \serial Tr. Mat. Inst. Steklova \yr 2019 \vol 304 \pages 174--204 \publ Steklov Math. Inst. RAS \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3966} \crossref{https://doi.org/10.4213/tm3966} \elib{http://elibrary.ru/item.asp?id=37461007} \transl \jour Proc. Steklov Inst. Math. \yr 2019 \vol 304 \pages 160--189 \crossref{https://doi.org/10.1134/S0081543819010127} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000470695400012} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85066784160}