Robust Asymptotic Stability of Desynchronization in Impulse-Coupled Oscillators
Robust Asymptotic Stability of Desynchronization in Impulse-Coupled Oscillators
复制标题
脉冲耦合振荡器失同步的鲁棒渐近稳定性
DOI：
10.1109/tcns.2015.2428308
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发表时间：
2015
影响因子：
4.2
通讯作者：
R. Sanfelice
中科院分区：
文献类型：
--
作者：
S. Phillips;R. Sanfelice
本文研究了齐次脉冲耦合振子全对全网络的去噪特性。每个脉冲耦合振荡器被建模为具有单个定时器状态的混合系统，该定时器状态在达到阈值时自复位到零，在该事件中，所有其他脉冲耦合振荡器按照共同的复位定律调整它们的定时器。在此设置中，解扰被认为是每个脉冲耦合振荡器的定时器在连续复位之间具有相等的间隔。我们表明，对于所考虑的模型，去奇异化是一个渐近稳定的属性。为此，我们重铸desertification作为一组稳定的问题，并采用混合动力系统的李雅普诺夫稳定性工具。此外，几个扰动被认为是一个强大的财产，desertification。连续和离散动力学的扰动被认为是。数值结果来说明的主要贡献。
The property of desynchronization in an all-to-all network of homogeneous impulse-coupled oscillators is studied. Each impulse-coupled oscillator is modeled as a hybrid system with a single timer state that self-resets to zero when it reaches a threshold, at which event all other impulse-coupled oscillators adjust their timers following a common reset law. In this setting, desynchronization is considered as each impulse-coupled oscillator's timer having equal separation between successive resets. We show that for the considered model, desynchronization is an asymptotically stable property. For this purpose, we recast desynchronization as a set stabilization problem and employ Lyapunov stability tools for hybrid systems. Furthermore, several perturbations are considered showing that desynchronization is a robust property. Perturbations on the continuous and discrete dynamics are considered. Numerical results are presented to illustrate the main contributions.