Local solutions of the fast-slow model of an optoelectronic oscillator with delay
type: Item
instance of: scholarly article
title: Local solutions of the fast-slow model of an optoelectronic oscillator with delay
zbMATH Open document ID: 1478.34088
DOI: 10.1134/S0040577921060040
author: D. V. Glazkov
published in: Theoretical and Mathematical Physics
publication date: 2021-08-23T00:00:00Z
review text: In this paper, the author studies the local dynamics of a difference-differential model of an optoelectronic oscillator (a modification of the Ikeda equation with delay) in a neighborhood of the zero equilibrium state. This model after the change of the variables and differentiation can be written in the form \[ \varepsilon \nu^{-1}\ddot x+\dot x+\nu x=b_1\dot x(t-1)+2b_2x(t-1)\dot x(t-1)+3b_3x^2(t-1)\dot x(t-1)+\cdots, \] \[ b_1=-\beta\sin(2\phi),\ b_2=-\beta\cos(2\phi),\ b_3=\frac23\beta\sin(2\phi), \] where the function \(x\) describes the voltage at the Mach-Zehnder modulator input, \(\beta\) is the feedback coefficient, \(\phi\) is the phase determining the operating point of the modulator, \(\varepsilon\) is the frequency cutoff coefficient and \(\nu\) is the delay time in the feedback circuit, which are both assumed to take small positive values. The dot denotes the derivative with respect to \(t.\) The author explicitly formulated results on the correspondence between the solutions of the original system and those of special equations for slow amplitudes, which play the role of normal forms.
reviewed by: Robert Vrabel
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K26
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 34K18
zbMATH DE Number: 7384148
zbMATH Keywords: differential equation
zbMATH Keywords: delay
zbMATH Keywords: small parameter
zbMATH Keywords: asymptotics
zbMATH Keywords: bifurcation
zbMATH Keywords: boundary value problem
MaRDI profile type: Publication
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full work available at URL: s0040577921060040
OpenAlex ID: W3176738575
description: scientific article; zbMATH DE number 7384148