On partial contraction analysis for coupled nonlinear oscillators

We describe a simple but 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, anti-synchronization 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 occur 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.

• Type: Journal
• Year: 2005
• Where: BC
• Authors: Wei Wang 0008, Jean-Jacques E. Slotine
• Keywords: BC 2005, Identical Nonlinear Oscillators, Nonlinear Contraction Theory, Synchronization