从振荡信号推断适用于同步与去同步系统的网络
Network inference applicable to both synchronous and desynchronous systems from oscillatory signals
AI总结：
本文提出一种基于相位约化理论、通过丢弃部分数据从时间序列推断同步与去同步振子网络的方法，并在极限环振子模拟数据上验证其有效性，拓展了网络推断的适用范围。
摘要：
同步现象在自然界中普遍存在，在数学上可由耦合振子描述。同步强烈依赖于相互作用网络，且该网络在调控动力学中起着关键作用。为了理解和控制现实世界中的同步动力学，从观测数据中识别网络至关重要。以往研究已经发展了推断异步系统网络的方法，但推断高度同步振子的网络仍然具有挑战性。在本研究中，我们提出了一种从时间序列推断同步与去同步振子网络的方法。我们的方法将网络推断的适用范围扩展到更广泛的振荡系统类别。所提方法丢弃了用于推断的大部分数据，这看似违反直觉。然而，该方法的有效性得到了相位约化理论的支持，该理论是弱耦合振子的成熟理论。我们通过将该方法应用于极限环振子的模拟数据来验证所提方法。本研究为从网络视角理解现实世界系统中的同步迈出了重要一步。
英文摘要：
Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand and control synchronization dynamics in the real world, it is essential to identify the network from the observed data. While previous studies have developed the methods for inferring the network of asynchronous systems, it remains challenging to infer the network of well-synchronized oscillators. In this study, we develop a method for inferring the network of synchronized and desynchronized oscillators from time series. Our method expands the applicability of network inference to a wider class of oscillatory systems. The proposed method discards a large part of data used for inference, which may seem counterintuitive. However, the effectiveness of the method is supported by the phase reduction theory, a well-established theory for weakly coupled oscillators. We verify the proposed method by applying it to simulated data of the limit-cycle oscillators. This study provides an important step towards understanding synchronization in real-world systems from a network perspective.
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