Journal of Nonlinear Science

, Volume 21, Issue 6, pp 875–895 | Cite as

On Bifurcations in Nonlinear Consensus Networks

  • Vaibhav Srivastava
  • Jeff Moehlis
  • Francesco Bullo
Article

Abstract

The theory of consensus dynamics is widely employed to study various linear behaviors in networked control systems. Moreover, nonlinear phenomena have been observed in animal groups, power networks and in other networked systems. These observations inspire the development in this paper of three novel approaches to define distributed nonlinear dynamical interactions. The resulting dynamical systems are akin to higher-order nonlinear consensus systems. Over connected undirected graphs, the resulting dynamical systems exhibit various interesting behaviors that we rigorously characterize.

Keywords

Consensus network Networked systems Bifurcation theory 

Mathematics Subject Classification (2000)

34C23 34K18 68M12 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Vaibhav Srivastava
    • 1
  • Jeff Moehlis
    • 1
  • Francesco Bullo
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of California Santa BarbaraSanta BarbaraUSA

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