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Delay-induced switched states in a slow-fast system.

ABSTRACT: We consider the two-component delay system ?x'(t)?=?-?x(t)?-?y(t)?+?f(x(t?-?1)), y'(t)?=??x(t) with small para- meters ?, ? 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 ????0 and/or ????0 facilitate our understanding of this phenomenon. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

SUBMITTER: Ruschel S

PROVIDER: S-EPMC6661330 | biostudies-literature | 2019 Sep

REPOSITORIES: biostudies-literature

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Delay-induced switched states in a slow-fast system.

Ruschel Stefan S Yanchuk Serhiy S

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 20190722 2153

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 lim ...[more]

PMID: 31329072

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