Invariant cone and synchronization state stability of the mean field models

Méthode du cône invariant et stabilité de l'état de synchronisation des systèmes du type champs-moyen.

W. Oukil (1) , Ph. Thieullen , A. Kessi

1 Université Yahia Fares de Médéa

In this article we prove the stability of mean field systems as 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 os-cillators and the distribution of the natural frequencies. In order to prove the main result, we introduce the positive invariant cone and we start by studying the linearized system. The method can be applied to others mean field models as the Kuramoto model.

Mots clés: mean field; interconnected sys- tems; Stability; coupled oscillators; Winfree model; synchronization; interconnected sys-tems

Domaines: Systèmes dynamiques [math.DS]

W. Oukil, Ph. Thieullen, A. Kessi. Invariant cone and synchronization state stability of the mean field models. Dynamical Systems, 2018, 34 (3), pp.422-433. ⟨10.1080/14689367.2018.1547683⟩. ⟨hal-01825009v2⟩