There are various synchronization phenomena (Synchronization or Consensus) in nature and science, such as the synchronous flashing of fireflies in the field at night, the spatiotemporal synchronization of network security public opinion information, the intelligent synchronization control of photoelectric systems, and neurons in the brain neural network. The collaborative effect of the intelligent unmanned system, the collaborative execution of tasks, etc. (see Figure 1). Synchronization refers to the ability of interacting subsystems and subunits to overcome the constraints of long-range, heterogeneity and other highly dynamic and complex environments to form a consistent dynamic process. Therefore, it is the key to maintaining the stability of the natural system and breaking through the stuck neck Technology and safeguarding human life and health have played a vital role. However, with the rapid development of the network and the emergence of massive amounts of data, the synchronization laws within and between systems have become more and more complicated and diversified, such as singular states, telesynchronization, and group synchronization, which puts forward the new challenge to traditional research: Is it possible to propose a unified framework that can accurately calculate and predict the synchronization laws of different dimensions and play a greater role in real engineering?
(a) The scene of fireflies glowing synchronously; (b) High-voltage grid synchronization; (c) Brain network synchronization.
In response to this challenge, Professor Li Xuelong and Professor Wang Zhen of NPU proposed a unified analysis framework for system synchronization, and conducted in-depth research on the laws of network synchronization in different dimensions. The research results “Discontinuous Transitions and Rhythmic States in the D-Dimensional Kuramoto Model Induced by a Positive Feedback with the Global Order Parameter” was recently published in the internationally renowned journal Physical Review Letters (PRL). Since its establishment in 1958, PRL has comprehensively reported the latest important research results of various research groups around the world that have a wide-ranging impact on the entire scientific research field. It has a high degree of attention in the fields of information, physics, mathematics, and life.
In this research, the team proposed a unified analysis and prediction framework for synchronization systems, which can be applied to network systems of different dimensions. They discovered a new phenomenon in the synchronization of high-dimensional coupled oscillators: synchronous phase transitions in all even-numbered dimensions. The middle is an explosive first-order phase transition (see Figure 2(a)); and in all odd dimensions, the phase transition process will go through a time-dependent and turbulent phase (see Figure 2(b)). The emergence of this kind of shock phenomenon breaks the traditional cognition and is significantly different from the results of the traditional two-dimensional synchronization framework. It can be applied to the security situation assessment of large-scale real networks, the optimization of the life and space-time characteristics of intelligent photoelectric systems, and the intelligence of unmanned systems. The regulation of decision-making provides direct support for the stability and phase change control of the economic, social, and military systems. In addition, the team also gave a precise mathematical analysis. This analytical framework will help to explore the new characteristics of time-dependent group dynamics in high-dimensional space, and this new discovery can provide a new idea for the study of unknown group behavior dynamics.
The synchronization rate varies with the coupling strength in even-numbered dimensions (a) and odd-numbered dimensions (b).
The first author and corresponding author of this work are both from the Optical Image Analysis and Learning Center (OPTIMAL) of the Academic Special Zone of NPU. Moreover, this is the first PRL article that both the author and the corresponding author have come from NPU since 2002. This work is also a series of innovations made by the team this year following the Proceedings of the National Academy of Sciences (PNAS), IEEE Transactions on Pattern Analysis and Machine Intelligence (IEEE TPAMI). What’s more, these research results will provide a new framework, reference and energy for engineering application research and theoretical originality research with NPU’s characteristics.
Article link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.194101
Writer: Dai Xiangfeng, Reviewer: Liu Yuanshan
