Ruschel Stefan, Yanchuk Serhiy
Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, 10587 Berlin, Germany.
Philos Trans A Math Phys Eng Sci. 2019 Sep 9;377(2153):20180118. doi: 10.1098/rsta.2018.0118. Epub 2019 Jul 22.
We consider the two-component delay system εx'(t) = - x(t) - y(t) + f(x(t - 1)), y'(t) = ηx(t) with small para- meters ε, η and positive feedback function f. Previously, such systems have been reported to model switching in optoelectronic experiments, where each switching induces another one after approximately one delay time, related to one round trip of the signal. In this paper, we study these delay-induced switched states. We provide conditions for their existence and show how the formal limits ε → 0 and/or η → 0 facilitate our understanding of this phenomenon. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.
我们考虑双分量延迟系统(\varepsilon x'(t) = - x(t) - y(t) + f(x(t - 1)))，(y'(t) = \eta x(t))，其中(\varepsilon)、(\eta)为小参数，(f)为正反馈函数。此前，据报道此类系统可用于模拟光电实验中的开关现象，在该实验中，每次开关在大约一个延迟时间后会引发另一次开关，这与信号的一次往返有关。在本文中，我们研究这些由延迟引起的开关状态。我们给出了它们存在的条件，并展示了形式极限(\varepsilon \to 0)和/或(\eta \to 0)如何有助于我们理解这一现象。本文是主题为“延迟系统的非线性动力学”的一部分。
