Invariant cone and synchronization state stability of the mean field models. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Oukil, W.; Thieullen, Ph.; Kessi, A.
• Is Part Of: Dynamical systems. Volume 34:Issue 3(2019)
• Page Start: 422
• Page End: 433
• Publication Date: 2019-07-03
• Subjects: Stability -- coupled oscillators -- mean field -- interconnected systems -- synchronization -- Winfree model; 37C75; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2018.1547683
• Languages: English
• ISSNs: 1468-9367

Abstract

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.