3 years ago

The mathematics of asymptotic stability in the Kuramoto model.

Helge Dietert, Bastien Fernandez

Now a standard in Nonlinear Sciences, the Kuramoto model epitomizes the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been predicted in early works on this model, the corresponding rigorous validation has long remained problematic and was achieved only recently. This paper reviews the mathematical results on asymptotic stability of stationary solutions (and also globally rotating ones, thanks to symmetries) in the continuum limit of the Kuramoto model, and provides insights into the principal arguments of proofs. Finally, in order to complete the theory, various examples, additional original results and some extensions to common developments of the model are also given.

Publisher URL: http://arxiv.org/abs/1801.01309

DOI: arXiv:1801.01309v2

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.