带随机扰动的耦合谐振子网络系统的同步

Synchronization of Networked Harmonic Oscillator Systems with Stochastic Perturbations

研究了一种带随机扰动输入项的耦合谐振子网络系统的同步动力学。针对实际工程应用中数据难免带有各种随机扰动等现象,基于相对位移信息耦合优点,设计了一个在一般条件下适用的分布式控制输入协议。利用随机微分方程的稳定性理论以及伊藤(It?)公式等工具,分析了耦合谐振子网络系统在这个协议下的同步动力学,得到了系统达到几乎处处同步的一个充分条件。数值模拟进一步验证了该理论结果的正确性和协议的有效性。

In this paper, the synchronization dynamics of a networked harmonic oscillators system with stochastic input terms was studied. Aiming at the stochastic perturbation of data in practical engineering application, a distributed control input protocol was designed based on the advantage of relative displacement information coupling. By using the stability theory of stochastic differential equation and It formula, the synchronization dynamics of networked harmonic oscillators system under this protocol is analyzed, and a sufficient condition for the system to achieve almost surely synchronization is obtained. The numerical simulations further verify the correctness of the theoretical results and the effectiveness of the protocol.