Robustness of synchronization to additive noise

how vulnerability depends on dynamics

Maurizio Porfiri, Mattia Frasca

Research output: Contribution to journalArticle

Abstract

From biological to technological networks, scientists and engineers must face the question of vulnerability to understand evolutionary processes or design resilient systems. Here, we examine the vulnerability of a network of coupled dynamical units to failure or malfunction of one of its nodes. More specifically, we study the effect of additive noise that is injected at one of the network sites on the overall synchronization of the coupled dynamical systems. In the context of mean square stochastic stability, we present a mathematically-principled approach to illuminate the interplay between dynamics and topology on network robustness. Through the new theoretical construct of robust metric, we uncover a complex and often counterintuitive effect of dynamics. While networks are more robust to noise injected at their hubs for a classical consensus problem, these hubs could become the most vulnerable nodes for higher order dynamics, such as second-order consensus and R\"{o}ssler chaos. From the exact treatment of star networks and the systematic application of perturbation techniques, we offer a mechanistic explanation of these surprising results and lay the foundati

Original languageEnglish (US)
JournalIEEE Transactions on Control of Network Systems
DOIs
StateAccepted/In press - Apr 7 2018

Fingerprint

Additive noise
Additive Noise
Robustness (control systems)
Vulnerability
Synchronization
Robustness
Perturbation techniques
Chaos theory
Stars
Dynamical systems
Topology
Engineers
Mean-square Stability
Consensus Problem
Stochastic Stability
Perturbation Technique
Vertex of a graph
Star
Chaos
Dynamical system

Keywords

  • Consensus
  • information centrality
  • mean square
  • nonlinear
  • perturbation
  • stochastic stability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Control and Optimization

Cite this

@article{9e4bc3ca4f9144dfba4ad968970aa113,
title = "Robustness of synchronization to additive noise: how vulnerability depends on dynamics",
abstract = "From biological to technological networks, scientists and engineers must face the question of vulnerability to understand evolutionary processes or design resilient systems. Here, we examine the vulnerability of a network of coupled dynamical units to failure or malfunction of one of its nodes. More specifically, we study the effect of additive noise that is injected at one of the network sites on the overall synchronization of the coupled dynamical systems. In the context of mean square stochastic stability, we present a mathematically-principled approach to illuminate the interplay between dynamics and topology on network robustness. Through the new theoretical construct of robust metric, we uncover a complex and often counterintuitive effect of dynamics. While networks are more robust to noise injected at their hubs for a classical consensus problem, these hubs could become the most vulnerable nodes for higher order dynamics, such as second-order consensus and R\{"}{o}ssler chaos. From the exact treatment of star networks and the systematic application of perturbation techniques, we offer a mechanistic explanation of these surprising results and lay the foundati",
keywords = "Consensus, information centrality, mean square, nonlinear, perturbation, stochastic stability",
author = "Maurizio Porfiri and Mattia Frasca",
year = "2018",
month = "4",
day = "7",
doi = "10.1109/TCNS.2018.2825024",
language = "English (US)",
journal = "IEEE Transactions on Control of Network Systems",
issn = "2325-5870",
publisher = "IEEE CONTROL SYSTEMS SOCIETY",

}

TY - JOUR

T1 - Robustness of synchronization to additive noise

T2 - how vulnerability depends on dynamics

AU - Porfiri, Maurizio

AU - Frasca, Mattia

PY - 2018/4/7

Y1 - 2018/4/7

N2 - From biological to technological networks, scientists and engineers must face the question of vulnerability to understand evolutionary processes or design resilient systems. Here, we examine the vulnerability of a network of coupled dynamical units to failure or malfunction of one of its nodes. More specifically, we study the effect of additive noise that is injected at one of the network sites on the overall synchronization of the coupled dynamical systems. In the context of mean square stochastic stability, we present a mathematically-principled approach to illuminate the interplay between dynamics and topology on network robustness. Through the new theoretical construct of robust metric, we uncover a complex and often counterintuitive effect of dynamics. While networks are more robust to noise injected at their hubs for a classical consensus problem, these hubs could become the most vulnerable nodes for higher order dynamics, such as second-order consensus and R\"{o}ssler chaos. From the exact treatment of star networks and the systematic application of perturbation techniques, we offer a mechanistic explanation of these surprising results and lay the foundati

AB - From biological to technological networks, scientists and engineers must face the question of vulnerability to understand evolutionary processes or design resilient systems. Here, we examine the vulnerability of a network of coupled dynamical units to failure or malfunction of one of its nodes. More specifically, we study the effect of additive noise that is injected at one of the network sites on the overall synchronization of the coupled dynamical systems. In the context of mean square stochastic stability, we present a mathematically-principled approach to illuminate the interplay between dynamics and topology on network robustness. Through the new theoretical construct of robust metric, we uncover a complex and often counterintuitive effect of dynamics. While networks are more robust to noise injected at their hubs for a classical consensus problem, these hubs could become the most vulnerable nodes for higher order dynamics, such as second-order consensus and R\"{o}ssler chaos. From the exact treatment of star networks and the systematic application of perturbation techniques, we offer a mechanistic explanation of these surprising results and lay the foundati

KW - Consensus

KW - information centrality

KW - mean square

KW - nonlinear

KW - perturbation

KW - stochastic stability

UR - http://www.scopus.com/inward/record.url?scp=85045204460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045204460&partnerID=8YFLogxK

U2 - 10.1109/TCNS.2018.2825024

DO - 10.1109/TCNS.2018.2825024

M3 - Article

JO - IEEE Transactions on Control of Network Systems

JF - IEEE Transactions on Control of Network Systems

SN - 2325-5870

ER -