TY - JOUR
T1 - Delay-induced switched states in a slow-fast system
AU - Ruschel, Stefan
AU - Yanchuk, Serhiy
N1 - Publisher Copyright:
© 2019 The Author(s) Published by the Royal Society. All rights reserved.
PY - 2019/9/9
Y1 - 2019/9/9
N2 - We consider the two-component delay system εx(t) = −x(t) − y(t) + f(x(t − 1)), y(t) = ηx(t) with small parameters 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'.
AB - We consider the two-component delay system εx(t) = −x(t) − y(t) + f(x(t − 1)), y(t) = ηx(t) with small parameters 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'.
KW - Delay differential equations
KW - Delay-induced switched states
KW - Slow-fast oscillations
UR - https://www.scopus.com/pages/publications/85069923121
U2 - 10.1098/rsta.2018.0118
DO - 10.1098/rsta.2018.0118
M3 - Article
C2 - 31329072
AN - SCOPUS:85069923121
SN - 1364-503X
VL - 377
JO - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
JF - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
IS - 2153
M1 - 2018118
ER -