Structure and dynamics of acyclic networks

Alan Veliz-Cuba; David Murrugarra; Reinhard Laubenbacher

doi:10.1007/s10626-013-0174-2

Structure and dynamics of acyclic networks

Alan Veliz-Cuba, David Murrugarra, Reinhard Laubenbacher

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 language	English
Pages (from-to)	647-658
Number of pages	12
Journal	Discrete Event Dynamic Systems: Theory and Applications
Volume	24
Issue number	4
DOIs	https://doi.org/10.1007/s10626-013-0174-2
State	Published - Oct 11 2014

Bibliographical note

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

Funding

This work was supported by the National Science Foundation under Grant

Funders	Funder number
National Science Foundation (NSF)

Keywords

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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10.1007/s10626-013-0174-2

Cite this

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title = "Structure and dynamics of acyclic networks",

abstract = "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.",

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T1 - Structure and dynamics of acyclic networks

AU - Veliz-Cuba, Alan

AU - Murrugarra, David

AU - Laubenbacher, Reinhard

PY - 2014/10/11

Y1 - 2014/10/11

N2 - 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.

AB - 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.

KW - Acyclic network

KW - Dependency graph

KW - Globally asymptotically stable

KW - Steady state

KW - Wiring diagram

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JO - Discrete Event Dynamic Systems: Theory and Applications

JF - Discrete Event Dynamic Systems: Theory and Applications

IS - 4

ER -

Structure and dynamics of acyclic networks

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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