http://orcid.org/0000-0002-1851-1496
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ABSTRACT
In this article we prove the stability of some mean field systems similar to the Winfree model in the synchronized state. The model is governed by the coupling strength parameter κ and the natural frequency of each oscillator. The stability is proved independently of the number of oscillators and the distribution of the natural frequencies. The main result is proved using the positive invariant cone method for the linearized system. This method can be applied to other mean field models as in the Kuramoto model.
2010 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgements
We would like to thank the referee for his/her precise remarks and corrections that helped us to improve the final text.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
W. Oukil http://orcid.org/0000-0002-1851-1496
Correction Statement
This article has been republished with minor changes. These changes do not impact the academic content of the article.