Crafting networks to achieve, or not achieve, chaotic states

Sarah De Nigris, Xavier Leoncini

Research output: Contribution to journalArticle

Abstract

The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links and the average eccentricity are controlled. This is done by rewiring links of a regular one-dimensional chain according to a probability p within a specific range r that can depend on the number of vertices N. We compute the thermodynamical behavior of a system defined on the network, the XY-rotors model, and monitor how it is affected by the topological changes. We identify the network effective dimension d as a crucial parameter: topologies with d<2 exhibit no phase transitions, while topologies with d>2 display a second-order phase transition. Topologies with d=2 exhibit states characterized by infinite susceptibility and macroscopic chaotic, turbulent dynamical behavior. These features are also captured by d in the finite size context.

Original languageEnglish
Article number042809
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume91
Issue number4
DOIs
Publication statusPublished - 27 Apr 2015

Fingerprint

Effective Dimension
Topology
topology
Eccentricity
Thermodynamic Limit
Dynamical Behavior
Network Topology
Susceptibility
Rotor
Network Model
Monitor
Phase Transition
Dynamical system
eccentricity
dynamical systems
Range of data
rotors
monitors
apexes
magnetic permeability

Cite this

@article{80b52e0163334aadb0c754cd25550579,
title = "Crafting networks to achieve, or not achieve, chaotic states",
abstract = "The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links and the average eccentricity are controlled. This is done by rewiring links of a regular one-dimensional chain according to a probability p within a specific range r that can depend on the number of vertices N. We compute the thermodynamical behavior of a system defined on the network, the XY-rotors model, and monitor how it is affected by the topological changes. We identify the network effective dimension d as a crucial parameter: topologies with d<2 exhibit no phase transitions, while topologies with d>2 display a second-order phase transition. Topologies with d=2 exhibit states characterized by infinite susceptibility and macroscopic chaotic, turbulent dynamical behavior. These features are also captured by d in the finite size context.",
author = "{De Nigris}, Sarah and Xavier Leoncini",
year = "2015",
month = "4",
day = "27",
doi = "10.1103/PhysRevE.91.042809",
language = "English",
volume = "91",
journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
issn = "1539-3755",
publisher = "American Physical Society",
number = "4",

}

Crafting networks to achieve, or not achieve, chaotic states. / De Nigris, Sarah; Leoncini, Xavier.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 91, No. 4, 042809, 27.04.2015.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Crafting networks to achieve, or not achieve, chaotic states

AU - De Nigris, Sarah

AU - Leoncini, Xavier

PY - 2015/4/27

Y1 - 2015/4/27

N2 - The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links and the average eccentricity are controlled. This is done by rewiring links of a regular one-dimensional chain according to a probability p within a specific range r that can depend on the number of vertices N. We compute the thermodynamical behavior of a system defined on the network, the XY-rotors model, and monitor how it is affected by the topological changes. We identify the network effective dimension d as a crucial parameter: topologies with d<2 exhibit no phase transitions, while topologies with d>2 display a second-order phase transition. Topologies with d=2 exhibit states characterized by infinite susceptibility and macroscopic chaotic, turbulent dynamical behavior. These features are also captured by d in the finite size context.

AB - The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links and the average eccentricity are controlled. This is done by rewiring links of a regular one-dimensional chain according to a probability p within a specific range r that can depend on the number of vertices N. We compute the thermodynamical behavior of a system defined on the network, the XY-rotors model, and monitor how it is affected by the topological changes. We identify the network effective dimension d as a crucial parameter: topologies with d<2 exhibit no phase transitions, while topologies with d>2 display a second-order phase transition. Topologies with d=2 exhibit states characterized by infinite susceptibility and macroscopic chaotic, turbulent dynamical behavior. These features are also captured by d in the finite size context.

UR - http://www.scopus.com/inward/record.url?scp=84929120709&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.91.042809

DO - 10.1103/PhysRevE.91.042809

M3 - Article

AN - SCOPUS:84929120709

VL - 91

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 4

M1 - 042809

ER -