Structure and dynamics of acyclic networks

Alan Veliz-Cuba, David Murrugarra, Reinhard Laubenbacher

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Acyclic networks are dynamical systems whose dependency graph (or wiring diagram) is an acyclic graph. It is known that such systems will have a unique steady state and that it will be globally asymptotically stable. Such result is independent of the mathematical framework used. More precisely, this result is true for discrete-time finite-space, discrete-time discrete-space, discrete-time continuous-space and continuous-time continuous-space dynamical systems; however, the proof of this result is dependent on the framework used. In this paper we present a novel and simple argument that works for all of these frameworks. Our arguments support the importance of the connection between structure and dynamics.

Original languageEnglish
Pages (from-to)647-658
Number of pages12
JournalDiscrete Event Dynamic Systems: Theory and Applications
Issue number4
StatePublished - Oct 11 2014

Bibliographical note

Publisher Copyright:
© 2013, Springer Science+Business Media New York.


  • Acyclic network
  • Dependency graph
  • Globally asymptotically stable
  • Steady state
  • Wiring diagram

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Electrical and Electronic Engineering


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