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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 304, Pages 174–204
DOI: https://doi.org/10.4213/tm3966 (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
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DOI: https://doi.org/10.4213/tm3966
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.
Received: March 18, 2018
Revised: September 14, 2018
Accepted: January 16, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 304, Pages 160–189
DOI: https://doi.org/10.1134/S0081543819010127
Bibliographic databases:
Document Type: Article
UDC: 517.926
Language: Russian
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, Trudy Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 174–204; Proc. Steklov Inst. Math., 304 (2019), 160–189
Citation in format AMSBIB
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\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 Trudy Mat. Inst. Steklova
\yr 2019
\vol 304
\pages 174--204
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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