Biological Cybernetics

, Volume 92, Issue 1, pp 38–53 | Cite as

On partial contraction analysis for coupled nonlinear oscillators

  • Wei Wang
  • Jean-Jacques E. SlotineEmail author


We describe a simple yet general method to analyze networks of coupled identical nonlinear oscillators and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized) results on synchronization, antisynchronization, and oscillator death. The method can be applied to coupled networks of various structures and arbitrary size. For oscillators with positive definite diffusion coupling, it can be shown that synchronization always occurs globally for strong enough coupling strengths, and an explicit upper bound on the corresponding threshold can be computed through eigenvalue analysis. The discussion also extends to the case when network structure varies abruptly and asynchronously, as in “flocks” of oscillators or dynamic elements.


Network Structure Coupling Strength Diffusion Coupling Nonlinear Oscillator Study Application 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Nonlinear Systems LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

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