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Updated: Aug 20, 2026

Fabrication and Testing of Microfluidic Optomechanical Oscillators
Published on: May 29, 2014
On partial contraction analysis for coupled nonlinear oscillators
Wei Wang1, Jean-Jacques E Slotine
1Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA, wangwei@mit.edu.
Abstract:
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.
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