### 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.

Language | English |
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Title of host publication | Nonlinear systems : techniques for dynamical analysis and control |

Editors | Nathan van de Wouw, Erjen Lefeber, Ines Lopez Arteaga |

Place of Publication | Berlin |

Publisher | Springer |

Chapter | 7 |

Pages | 137-154 |

Number of pages | 18 |

ISBN (Electronic) | 978-3-319-30357-4 |

ISBN (Print) | 978-3-319-30356-7 |

DOIs | |

State | Published - 2017 |

Event | International workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016 - Eindhoven, Netherlands Duration: 21 Jan 2016 → 21 Jan 2016 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Volume | 470 |

ISSN (Print) | 01708643 |

### Conference

Conference | International workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016 |
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Country | Netherlands |

City | Eindhoven |

Period | 21/01/16 → 21/01/16 |

### Fingerprint

### Cite this

*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

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Emergence of oscillations in networks of time-delay coupled inert systems

AU - Steur,E.

AU - Pogromskiy,S.

PY - 2017

Y1 - 2017

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84978540229&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-30357-4_7

DO - 10.1007/978-3-319-30357-4_7

M3 - Chapter

SN - 978-3-319-30356-7

T3 - Lecture Notes in Control and Information Sciences

SP - 137

EP - 154

BT - Nonlinear systems : techniques for dynamical analysis and control

PB - Springer

CY - Berlin

ER -