Emergence of oscillations in networks of time-delay coupled inert systems

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

We discuss the emergence of oscillations in networks of single-input- single-output systems that interact via linear time-delay coupling functions.Although the systems itself are inert, that is, their solutions converge to a globally stable equilibrium, in the presence of coupling, the network of systems exhibits ongoing oscillatory activity.We address the problem of emergence of oscillations by deriving conditions for; 1. solutions of the time-delay coupled systems to be bounded, 2. the network equilibrium to be unique, and 3. the network equilibrium to be unstable. If these conditions are all satisfied, the time-delay coupled inert systems have a nontrivial oscillatory solution. In addition, we show that a necessary condition for the emergence of oscillations in such networks is that the considered systems are at least of second order.

LanguageEnglish
Title of host publicationNonlinear systems : techniques for dynamical analysis and control
EditorsNathan van de Wouw, Erjen Lefeber, Ines Lopez Arteaga
Place of PublicationBerlin
PublisherSpringer
Chapter7
Pages137-154
Number of pages18
ISBN (Electronic)978-3-319-30357-4
ISBN (Print)978-3-319-30356-7
DOIs
StatePublished - 2017
EventInternational workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016 - Eindhoven, Netherlands
Duration: 21 Jan 201621 Jan 2016

Publication series

NameLecture Notes in Control and Information Sciences
Volume470
ISSN (Print)01708643

Conference

ConferenceInternational workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016
CountryNetherlands
CityEindhoven
Period21/01/1621/01/16

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Steur, E., & Pogromskiy, S. (2017). Emergence of oscillations in networks of time-delay coupled inert systems. In N. van de Wouw, E. Lefeber, & I. Lopez Arteaga (Eds.), Nonlinear systems : techniques for dynamical analysis and control (pp. 137-154). (Lecture Notes in Control and Information Sciences; Vol. 470). Berlin: Springer. DOI: 10.1007/978-3-319-30357-4_7
Steur, E. ; Pogromskiy, S./ Emergence of oscillations in networks of time-delay coupled inert systems. Nonlinear systems : techniques for dynamical analysis and control. editor / Nathan van de Wouw ; Erjen Lefeber ; Ines Lopez Arteaga. Berlin : Springer, 2017. pp. 137-154 (Lecture Notes in Control and Information Sciences).
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Steur, E & Pogromskiy, S 2017, Emergence of oscillations in networks of time-delay coupled inert systems. in N van de Wouw, E Lefeber & I Lopez Arteaga (eds), Nonlinear systems : techniques for dynamical analysis and control. Lecture Notes in Control and Information Sciences, vol. 470, Springer, Berlin, pp. 137-154, International workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016, Eindhoven, Netherlands, 21/01/16. DOI: 10.1007/978-3-319-30357-4_7

Emergence of oscillations in networks of time-delay coupled inert systems. / Steur, E.; Pogromskiy, S.

Nonlinear systems : techniques for dynamical analysis and control. ed. / Nathan van de Wouw; Erjen Lefeber; Ines Lopez Arteaga. Berlin : Springer, 2017. p. 137-154 (Lecture Notes in Control and Information Sciences; Vol. 470).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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AB - We discuss the emergence of oscillations in networks of single-input- single-output systems that interact via linear time-delay coupling functions.Although the systems itself are inert, that is, their solutions converge to a globally stable equilibrium, in the presence of coupling, the network of systems exhibits ongoing oscillatory activity.We address the problem of emergence of oscillations by deriving conditions for; 1. solutions of the time-delay coupled systems to be bounded, 2. the network equilibrium to be unique, and 3. the network equilibrium to be unstable. If these conditions are all satisfied, the time-delay coupled inert systems have a nontrivial oscillatory solution. In addition, we show that a necessary condition for the emergence of oscillations in such networks is that the considered systems are at least of second order.

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Steur E, Pogromskiy S. Emergence of oscillations in networks of time-delay coupled inert systems. In van de Wouw N, Lefeber E, Lopez Arteaga I, editors, Nonlinear systems : techniques for dynamical analysis and control. Berlin: Springer. 2017. p. 137-154. (Lecture Notes in Control and Information Sciences). Available from, DOI: 10.1007/978-3-319-30357-4_7