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] Scott R. Pope, Laura M. Ellwein, Cheryl L. Zapata, Vera Novak, C. T. Kelley, Mette S. Olufsen . Estimation and identification of parameters in a lumped cerebrovascular model. Mathematical Biosciences and Engineering, 2009, 6(1): 93-115. doi: 10.3934/mbe.2009.6.93
    [2] Benchawan Wiwatanapataphee, Yong Hong Wu, Thanongchai Siriapisith, Buraskorn Nuntadilok . Effect of branchings on blood flow in the system of human coronary arteries. Mathematical Biosciences and Engineering, 2012, 9(1): 199-214. doi: 10.3934/mbe.2012.9.199
    [3] B. Wiwatanapataphee, D. Poltem, Yong Hong Wu, Y. Lenbury . Simulation of Pulsatile Flow of Blood in Stenosed Coronary Artery Bypass with Graft. Mathematical Biosciences and Engineering, 2006, 3(2): 371-383. doi: 10.3934/mbe.2006.3.371
    [4] Panagiotes A. Voltairas, Antonios Charalambopoulos, Dimitrios I. Fotiadis, Lambros K. Michalis . A quasi-lumped model for the peripheral distortion of the arterial pulse. Mathematical Biosciences and Engineering, 2012, 9(1): 175-198. doi: 10.3934/mbe.2012.9.175
    [5] Mette S. Olufsen, Ali Nadim . On deriving lumped models for blood flow and pressure in the systemic arteries. Mathematical Biosciences and Engineering, 2004, 1(1): 61-80. doi: 10.3934/mbe.2004.1.61
    [6] Meiyuan Du, Chi Zhang, Sheng Xie, Fang Pu, Da Zhang, Deyu Li . Investigation on aortic hemodynamics based on physics-informed neural network. Mathematical Biosciences and Engineering, 2023, 20(7): 11545-11567. doi: 10.3934/mbe.2023512
    [7] Fan He, Minru Li, Xinyu Wang, Lu Hua, Tingting Guo . Numerical investigation of quantitative pulmonary pressure ratio in different degrees of stenosis. Mathematical Biosciences and Engineering, 2024, 21(2): 1806-1818. doi: 10.3934/mbe.2024078
    [8] Giovanna Guidoboni, Alon Harris, Lucia Carichino, Yoel Arieli, Brent A. Siesky . Effect of intraocular pressure on the hemodynamics of the central retinal artery: A mathematical model. Mathematical Biosciences and Engineering, 2014, 11(3): 523-546. doi: 10.3934/mbe.2014.11.523
    [9] Yubo Sun, Yuanyuan Cheng, Yugen You, Yue Wang, Zhizhong Zhu, Yang Yu, Jianda Han, Jialing Wu, Ningbo Yu . A novel plantar pressure analysis method to signify gait dynamics in Parkinson's disease. Mathematical Biosciences and Engineering, 2023, 20(8): 13474-13490. doi: 10.3934/mbe.2023601
    [10] Alessandro Bertuzzi, Antonio Fasano, Alberto Gandolfi, Carmela Sinisgalli . Interstitial Pressure And Fluid Motion In Tumor Cords. Mathematical Biosciences and Engineering, 2005, 2(3): 445-460. doi: 10.3934/mbe.2005.2.445
  • 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.


  • 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(2831) 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