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This article is cited in 3 scientific papers (total in 3 papers)
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 “MEPhI”, 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.
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
Linking options:
https://www.mathnet.ru/eng/zvmmf10031 https://www.mathnet.ru/eng/zvmmf/v54/i5/p766
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Abstract page: | 313 | Full-text PDF : | 63 | References: | 82 | First page: | 22 |
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