Loading [Contrib]/a11y/accessibility-menu.js
Search Advanced

Mathematical Biosciences and Engineering

2010, Volume 7, Issue 3: 623-639. doi: 10.3934/mbe.2010.7.623
Previous Article Next Article

Local stabilization and network synchronization: The case of stationary regimes

  • 1.
    DEI, Politecnico di Milano Via Ponzio 34/5 20133 Milano
  • Received: 01 October 2009 Accepted: 29 June 2018 Published: 01 June 2010

  • MSC : Primary: 37B25, 92B05, 92D25; Secondary: 34A34, 37C75, 92D40.

  • Relationships between local stability and synchronization in networks of identical dynamical systems are established through the Master Stability Function approach. First, it is shown that stable equilibria of the local dynamics correspond to stable stationary synchronous regimes of the entire network if the coupling among the systems is sufficiently weak or balanced (in other words, stationary synchronous regimes can be unstable only if the coupling is sufficiently large and unbalanced). Then, it is shown that [de]stabilizing factors at local scale are [de]synchronizing at global scale again if the coupling is sufficiently weak or balanced. These results allow one to transfer, with almost no effort, what is known for simple prototypical models in biology and engineering to complex networks composed of these models. This is shown through a series of applications ranging from networks of electrical circuits to various problems in ecology and sociology involving migrations of plants, animal and human populations.

    Citation: Stefano Fasani, Sergio Rinaldi. Local stabilization and network synchronization: The case of stationary regimes[J]. Mathematical Biosciences and Engineering, 2010, 7(3): 623-639. doi: 10.3934/mbe.2010.7.623

    Related Papers:

    [1] Boqiang Chen, Zhizhou Zhu, Qiong Li, Daihai He . Resurgence of different influenza types in China and the US in 2021. Mathematical Biosciences and Engineering, 2023, 20(4): 6327-6333. doi: 10.3934/mbe.2023273
    [2] Eunha Shim . Prioritization of delayed vaccination for pandemic influenza. Mathematical Biosciences and Engineering, 2011, 8(1): 95-112. doi: 10.3934/mbe.2011.8.95
    [3] Olivia Prosper, Omar Saucedo, Doria Thompson, Griselle Torres-Garcia, Xiaohong Wang, Carlos Castillo-Chavez . Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza. Mathematical Biosciences and Engineering, 2011, 8(1): 141-170. doi: 10.3934/mbe.2011.8.141
    [4] Rodolfo Acuňa-Soto, Luis Castaňeda-Davila, Gerardo Chowell . A perspective on the 2009 A/H1N1 influenza pandemic in Mexico. Mathematical Biosciences and Engineering, 2011, 8(1): 223-238. doi: 10.3934/mbe.2011.8.223
    [5] Oren Barnea, Rami Yaari, Guy Katriel, Lewi Stone . Modelling seasonal influenza in Israel. Mathematical Biosciences and Engineering, 2011, 8(2): 561-573. doi: 10.3934/mbe.2011.8.561
    [6] Gerardo Chowell, Catherine E. Ammon, Nicolas W. Hengartner, James M. Hyman . Estimating the reproduction number from the initial phase of the Spanish flu pandemic waves in Geneva, Switzerland. Mathematical Biosciences and Engineering, 2007, 4(3): 457-470. doi: 10.3934/mbe.2007.4.457
    [7] Marco Arieli Herrera-Valdez, Maytee Cruz-Aponte, Carlos Castillo-Chavez . Multiple outbreaks for the same pandemic: Local transportation and social distancing explain the different "waves" of A-H1N1pdm cases observed in México during 2009. Mathematical Biosciences and Engineering, 2011, 8(1): 21-48. doi: 10.3934/mbe.2011.8.21
    [8] Hiroshi Nishiura . Joint quantification of transmission dynamics and diagnostic accuracy applied to influenza. Mathematical Biosciences and Engineering, 2011, 8(1): 49-64. doi: 10.3934/mbe.2011.8.49
    [9] Eunha Shim . Optimal strategies of social distancing and vaccination against seasonal influenza. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1615-1634. doi: 10.3934/mbe.2013.10.1615
    [10] Julien Arino, Chris Bauch, Fred Brauer, S. Michelle Driedger, Amy L. Greer, S.M. Moghadas, Nick J. Pizzi, Beate Sander, Ashleigh Tuite, P. van den Driessche, James Watmough, Jianhong Wu, Ping Yan . Pandemic influenza: Modelling and public health perspectives. Mathematical Biosciences and Engineering, 2011, 8(1): 1-20. doi: 10.3934/mbe.2011.8.1
  • Relationships between local stability and synchronization in networks of identical dynamical systems are established through the Master Stability Function approach. First, it is shown that stable equilibria of the local dynamics correspond to stable stationary synchronous regimes of the entire network if the coupling among the systems is sufficiently weak or balanced (in other words, stationary synchronous regimes can be unstable only if the coupling is sufficiently large and unbalanced). Then, it is shown that [de]stabilizing factors at local scale are [de]synchronizing at global scale again if the coupling is sufficiently weak or balanced. These results allow one to transfer, with almost no effort, what is known for simple prototypical models in biology and engineering to complex networks composed of these models. This is shown through a series of applications ranging from networks of electrical circuits to various problems in ecology and sociology involving migrations of plants, animal and human populations.


  • This article has been cited by:

    1. Eungyeong Kim, Seok Lee, Young Tae Byun, Hyuk-Jae Lee, Taikjin Lee, Implementation of integrated monitoring system for trace and path prediction of infectious disease, 2013, 14, 1598-0170, 69, 10.7472/jksii.2013.14.5.69
    2. Sergio A. Hojman, Felipe A. Asenjo, Phenomenological dynamics of COVID-19 pandemic: Meta-analysis for adjustment parameters, 2020, 30, 1054-1500, 103120, 10.1063/5.0019742
    3. S. Towers, G. Chowell, Impact of weekday social contact patterns on the modeling of influenza transmission, and determination of the influenza latent period, 2012, 312, 00225193, 87, 10.1016/j.jtbi.2012.07.023
    4. Kirsty J. Bolton, James M. McCaw, Mathew P. Dafilis, Jodie McVernon, Jane M. Heffernan, Seasonality as a driver of pH1N12009 influenza vaccination campaign impact, 2023, 17554365, 100730, 10.1016/j.epidem.2023.100730
    5. Thassakorn Sawetsuthipan, Naraphorn Paoprasert, Papis Wongchaisuwat, A stochastic game model for infectious disease management decisions in schools, 2024, 10293132, 100343, 10.1016/j.apmrv.2024.12.007
  • Reader Comments
  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(2824) PDF downloads(509) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog