Yipeng Shao, Yinghua Jin*, Aihua Hu, and Shuobing Yang
International Journal of Control, Automation, and Systems, vol. 20, no. 12, pp.3903-3914, 2022

Abstract : Each oscillator, subject to external fields, interacts with all the other oscillators. Therefore, the original thermodynamic Kuramoto model (TK model) is used to study the influence of some external fields upon its cooperative behavior. Three kinds of external fields are applied to the system: (a) random noises, (b) periodic force, (c) random noises and periodic force, so as to discuss TK model¡¯s cooperative behavior under external fields. In some adequate frameworks formulated with initial data and system parameters, the model exhibits cooperative dynamics.

Keyword : Additive white noise, asymptotic synchronicity, multiplicative white noise, periodic force, TK model.