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.

中文翻译：

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平均场模型的不变锥和同步状态稳定性

摘要 在本文中，我们证明了一些类似于 Winfree 模型的平均场系统在同步状态下的稳定性。该模型由耦合强度参数 κ 和每个振荡器的固有频率控制。稳定性的证明与振荡器的数量和固有频率的分布无关。对线性化系统采用正不变锥法证明了主要结果。这种方法可以应用于仓本模型中的其他平均场模型。