AI Article Synopsis
- This paper presents a method for analyzing networks of coupled nonlinear oscillators, focusing on synchronization, antisynchronization, and oscillator death.
- The approach uses nonlinear contraction theory, yielding exact global results applicable to various network structures and sizes.
- Findings indicate that with sufficiently strong coupling, synchronization can be guaranteed, and the paper also addresses scenarios with irregular and asynchronous network structures, relevant to systems like flocks of oscillators.
Article 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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| http://dx.doi.org/10.1007/s00422-004-0527-x | DOI Listing |
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