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This article is cited in 1 scientific paper (total in 1 paper)
The Buffer Phenomenon in One-Dimensional Piecewise Linear Mapping in Radiophysics
S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
We study the problem of attractors of the two-dimensional mapping
$$
(u,v)\to(v,-(1-\mu)u-F(v)),\qquad
F(v)=\begin{cases}
\hphantom{-}q_1&\text{for }v>0,
\\
\hphantom{-}0&\text{for }v=0,
\\
-q_2&\text{for }v<0,
\end{cases}
$$
where $0<\mu\ll1$ and $q_1,q_2>0$. This mapping is the mathematical model of a self-excited oscillator with relay amplifier and a part of the long transmission line without distortions in the feedback circuit. We prove that, in the system under study, there coexist stable cycles with arbitrarily large periods as the parameter $\mu$ decreases properly. We also show that the total number of these cycles increases without bound as $\mu\to0$, i.e., the buffer phenomenon is realized.
Keywords:
feedback circuit, boundary-value problem, attractor, stable (unstable) cycle, self-excited oscillator, buffer phenomenon, Lyapunov stability.
Received: 30.03.2005 Revised: 09.02.2006
Citation:
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “The Buffer Phenomenon in One-Dimensional Piecewise Linear Mapping in Radiophysics”, Mat. Zametki, 81:4 (2007), 507–514; Math. Notes, 81:4 (2007), 449–455
Linking options:
https://www.mathnet.ru/eng/mzm3693https://doi.org/10.4213/mzm3693 https://www.mathnet.ru/eng/mzm/v81/i4/p507
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Abstract page: | 396 | Full-text PDF : | 166 | References: | 50 | First page: | 9 |
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