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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 5, Pages 135–164 (Mi izv213)  

This article is cited in 8 scientific papers (total in 8 papers)

The diffusion-buffer phenomenon in a mathematical model of biology

A. Yu. Kolesova, N. Kh. Rozovb

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

Abstract: We consider the Neumann problem for partial differential-difference equations with diffusion that models a predator-prey problem. Using infinite-dimensional normalization, we establish the diffusion-buffer phenomenon, which means that the system can have any number of stable spatially inhomogeneous cycles if its parameters are properly chosen.

DOI: https://doi.org/10.4213/im213

Full text: PDF file (2006 kB)
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English version:
Izvestiya: Mathematics, 1998, 62:5, 985–1012

Bibliographic databases:

MSC: 35K50, 35B25, 35B10, 35C20
Received: 04.11.1996

Citation: A. Yu. Kolesov, N. Kh. Rozov, “The diffusion-buffer phenomenon in a mathematical model of biology”, Izv. RAN. Ser. Mat., 62:5 (1998), 135–164; Izv. Math., 62:5 (1998), 985–1012

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. A. Yu. Kolesov, N. Kh. Rozov, “Characteristic features of the dynamics of the Ginzburg–Landau equation in a plane domain”, Theoret. and Math. Phys., 125:2 (2000), 1476–1488  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “The buffer property in resonance systems of non-linear hyperbolic equations”, Russian Math. Surveys, 55:2 (2000), 297–321  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. A. Yu. Kolesov, N. Kh. Rozov, “Two-Frequency Autowave Processes in the Complex Ginzburg–Landau Equation”, Theoret. and Math. Phys., 134:3 (2003), 308–325  mathnet  crossref  crossref  mathscinet  isi
    4. A. Yu. Kolesov, N. Kh. Rozov, “The existence of countably many stable cycles for a generalized cubic Schrödinger equation in a planar domain”, Izv. Math., 67:6 (2003), 1213–1242  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. A. Yu. Kolesov, N. Kh. Rozov, “On the theoretical explanation of the diffusion buffer phenomenon”, Comput. Math. Math. Phys., 44:11 (2004), 1922–1941  mathnet  mathscinet  zmath  elib
    6. A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Buffer Phenomenon in Nonlinear Physics”, Proc. Steklov Inst. Math., 250 (2005), 102–168  mathnet  mathscinet  zmath
    7. N. Kh. Rozov, “Fenomen bufernosti v matematicheskikh modelyakh estestvoznaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2010, no. 3, 58–63  mathnet  elib
    8. 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, eds. Klein O., Dimian M., Gurevich P., Knees D., Rachinskii D., Tikhomirov S., IOP Publishing Ltd, 2016, UNSP 012004  crossref  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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