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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 5, Pages 766–778 (Mi zvmmf10031)  

Dynamics of the logistic delay equation with a large spatially distributed control coefficient

I. S. Kashchenkoa, S. A. Kashchenkob

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

Abstract: The local dynamics of the logistic delay equation with a large spatially distributed control coefficient is asymptotically studied. The basic bifurcation scenarios are analyzed depending on the relations between the parameters of the equation. It is shown that the equilibrium states can lose stability even for asymptotically small values of the delay parameter. The corresponding critical cases can have an infinite dimension. Special nonlinear parabolic equations are constructed whose nonlocal dynamics determine the local behavior of solutions to the original boundary value problem.

Key words: dynamics of the logistic delay equation, spatially distributed control, bifurcation, asymptotic methods, parabolic equations.

DOI: https://doi.org/10.7868/S0044466914050123

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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:5, 785–796

Bibliographic databases:

UDC: 519.62
Received: 18.11.2013

Citation: I. S. Kashchenko, S. A. Kashchenko, “Dynamics of the logistic delay equation with a large spatially distributed control coefficient”, Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014), 766–778; Comput. Math. Math. Phys., 54:5 (2014), 785–796

Citation in format AMSBIB
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