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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 1, Pages 76–89 (Mi zvmmf53)  
This article is cited in 15 scientific papers (total in 15 papers)

Extremal dynamics of the generalized Hutchinson equation

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

a Faculty of Mathematics, Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia
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Abstract: A scalar nonlinear differential-difference equation with two delays that generalizes Hutchinson's equation is considered. The bifurcation of self-oscillations of this equation from the zero equilibrium is studied in the extremal situation when one delay is asymptotically large while the other parameters are on the order of unity. Analytical methods combined with numerical techniques are used to show that the well-known buffer phenomenon occurs in the equation in this case. This means that an arbitrary finite number of different attractors coexist in the phase space of the equation with suitably chosen parameters.
Key words: differential-difference equation, bifurcation, quasi-normal form, buffer phenomenon.
Received: 13.02.2008
Revised: 20.03.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 1, Pages 71–83
DOI: https://doi.org/10.1134/S0965542509010059
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Extremal dynamics of the generalized Hutchinson equation”, Zh. Vychisl. Mat. Mat. Fiz., 49:1 (2009), 76–89; Comput. Math. Math. Phys., 49:1 (2009), 71–83
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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