Geodesic
The Buffer Phenomenon in One-Dimensional Piecewise Linear Mapping in Radiophysics
Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 507-514.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the problem of attractors of the two-dimensional mapping $$ (u,v)\to(v,-(1-\mu)u-F(v)),\qquad F(v)=\begin{cases} \hphantom{-}q_1\text{for }v>0, \\ \hphantom{-}0\text{for }v=0, \\ -q_2\text{for }v0, \end{cases} $$ 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. 
@article{MZM_2007_81_4_a3,
     author = {S. D. Glyzin and A. Yu. Kolesov and N. Kh. Rozov},
     title = {The {Buffer} {Phenomenon} in {One-Dimensional} {Piecewise} {Linear} {Mapping} in {Radiophysics}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {507--514},
     publisher = {mathdoc},
     volume = {81},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a3/}
}
TY  - JOUR
AU  - S. D. Glyzin
AU  - A. Yu. Kolesov
AU  - N. Kh. Rozov
TI  - The Buffer Phenomenon in One-Dimensional Piecewise Linear Mapping in Radiophysics
JO  - Matematičeskie zametki
PY  - 2007
SP  - 507
EP  - 514
VL  - 81
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a3/
LA  - ru
ID  - MZM_2007_81_4_a3
ER  - 
%0 Journal Article
%A S. D. Glyzin
%A A. Yu. Kolesov
%A N. Kh. Rozov
%T The Buffer Phenomenon in One-Dimensional Piecewise Linear Mapping in Radiophysics
%J Matematičeskie zametki
%D 2007
%P 507-514
%V 81
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a3/
%G ru
%F MZM_2007_81_4_a3
S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. The Buffer Phenomenon in One-Dimensional Piecewise Linear Mapping in Radiophysics. Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 507-514. http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a3/

[1] A. Yu. Kolesov, E. F. Mischenko, N. Kh. Rozov, “Asimptoticheskie metody issledovaniya periodicheskikh reshenii nelineinykh giperbolicheskikh uravnenii”, Tr. MIAN, 222 (1998), 7–191 | MR | Zbl

[2] A. Yu. Kolesov, N. Kh. Rozov, “Avtokolebaniya v RCLG-linii s malymi iskazheniyami”, Differents. uravneniya, 34:11 (1998), 1559–1561 | MR | Zbl

[3] A. Yu. Kolesov, N. Kh. Rozov, “Yavlenie bufernosti v RCLG-avtogeneratore: teoreticheskii analiz i rezultaty eksperimenta”, Tr. MIAN, 233 (2001), 153–207 | MR | Zbl

[4] A. N. Sharkovskii, Yu. L. Maistrenko, E. Yu. Romanenko, Raznostnye uravneniya i ikh prilozheniya, Naukova dumka, Kiev, 1986 | MR | Zbl