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

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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. 
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/
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     title = {The {Buffer} {Phenomenon} in {One-Dimensional} {Piecewise} {Linear} {Mapping} in {Radiophysics}},
     journal = {Matemati\v{c}eskie zametki},
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