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 Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 6, Pages 953–968 (Mi zvmmf10048)

Spatially distributed control of the dynamics of the logistic delay equation

D. S. Glyzina, S. A. Kashchenkoab

a Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia
b National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: The influence exerted by a small spatially inhomogeneous control on the dynamics of the logistic delay equation is studied. This paper consists of two parts. The first deals with the case where the logistic delay equation has a stable relaxation cycle. It is shown that a small control function can give rise to complex relaxation objects, namely, to a large number of different attractors. In the second part, the local dynamics of the stability problem is analyzed in a neighborhood of equilibrium in a close-to-critical case of “infinite” dimension. Special quasi-normal forms are constructed whose nonlocal dynamics determine the local behavior of solutions to the original equation. Some results of a numerical analysis are presented.

Key words: asymptotic methods, distributed Hutchinson equation, dynamics of the logistic delay equation, spatially inhomogeneous control.

DOI: https://doi.org/10.7868/S004446691406009X

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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:6, 963–976

Bibliographic databases:

UDC: 519.632
MSC: 34K25 (34C26 35F20 35R10 92D25)

Citation: D. S. Glyzin, S. A. Kashchenko, “Spatially distributed control of the dynamics of the logistic delay equation”, Zh. Vychisl. Mat. Mat. Fiz., 54:6 (2014), 953–968; Comput. Math. Math. Phys., 54:6 (2014), 963–976

Citation in format AMSBIB
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