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Modelirovanie i Analiz Informatsionnykh Sistem, 2014, Volume 21, Number 3, Pages 121–128
(Mi mais381)
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This article is cited in 1 scientific paper (total in 1 paper)
Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating Delay
N. D. Bykovaab a National Research Nuclear University MEPhI, Kashirskoye shosse 31, Moscow, 115409, Russia
b P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia
Abstract:
We consider the local dynamic of the logistic equation with rapidly oscillating time-periodic piecewise constant or piecewise linear coefficient of delay. It was shown that the averaged equation is a logistic equation with two delays in first case and logistic equation with distributed delay in second case. The criterion of equilibrium point stability was obtained in both cases. Dynamical properties of the original equation were considered in the critical case of equilibrium point of averaged equation stability problem. It was shown, that local dynamic in the critical case is defined by Lyapunov value whose sign depends on the parameters of the problem.
Keywords:
averaging, stability, nonlinear dynamics, normal form.
Received: 02.04.2014
Citation:
N. D. Bykova, “Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating Delay”, Model. Anal. Inform. Sist., 21:3 (2014), 121–128
Linking options:
https://www.mathnet.ru/eng/mais381 https://www.mathnet.ru/eng/mais/v21/i3/p121
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Abstract page: | 237 | Full-text PDF : | 99 | References: | 42 |
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