Title :

Infrastructure adaptation and emergence of loops in network routing with time-dependent loads

Author(s) :

Lonardi, Alessandro [Auteur]
Max Planck Institute for Intelligent Systems [Tübingen]
Facca, Enrico [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Putti, Mario [Auteur]
Dipartimento di Matematica [Padova]
de Bacco, Caterina [Auteur]
Santa Fe Institute
Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS]

Journal title :

Physical Review E

Pages :

024302

Publisher :

American Physical Society (APS)

Publication date :

2023-02-03

ISSN :

2470-0045

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Network routing approaches are widely used to study the evolution in time of self-adapting systems. However, few advances have been made for problems where adaptation is governed by time-dependent inputs. In this work we ...
Show more >Network routing approaches are widely used to study the evolution in time of self-adapting systems. However, few advances have been made for problems where adaptation is governed by time-dependent inputs. In this work we study a dynamical system where the edge conductivities of a network are regulated by time-varying mass loads injected on nodes. Motivated by empirical observations, we assume that conductivities adapt slowly with respect to the characteristic time of the loads. Furthermore, assuming the loads to be periodic, we derive a dynamics where the evolution of the system is controlled by a matrix obtained with the Fourier coefficients of the input loads. Remarkably, we find a sufficient condition on these coefficients that determines when the resulting network topologies are trees. We show an example of this on the Bordeaux bus network where we tune the input loads to interpolate between loopy and tree topologies. We validate our model on several synthetic networks and provide an expression for long-time solutions of the original conductivities.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL