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.
|Number of pages||12|
|Journal||Discrete Event Dynamic Systems: Theory and Applications|
|State||Published - Oct 11 2014|
Bibliographical noteFunding Information:
This work was supported by the National Science Foundation under Grant
© 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