Understanding Synchronization of Business Cycles Using Wavelet Analysis and Nonlinear Coupled Oscillator Models

通过对日本的工业生产指数进行小波分析，对于所有县对，我们得到了一个“距离”矩阵来表示商业周期同步程度是高还是低。此外，通过将各时间点同步水平较高的一组县作为一个集群，并检查其数量的时间变化，可以观察到经济衰退时期，特别是泡沫破裂后，同步水平比乐观时期更高。这种同步水平随时间变化的现象在区域商业周期模型中被强有力地观察到为“混沌流动”，在该模型中，所有区域都是同质的，并通过生产者的期望相互联系。混沌运动是高维动力系统中的复杂行为，混沌轨迹在许多不同的有序状态之间表现出巡回运动。

By applying wavelet analysis to Japan's industrial production indices, for all pairs of prefectures, we obtained a matrix of 'distance' to express whether the degree of business-cycle-synchronization was high or low. In addition, by considering a set of prefectures with high synchronization level at each time point as a cluster, and checking the time change of its number, it was observed that the synchronization level became higher in the economic recession period, especially after a bubble burst, than in the upbeat period. This kind of phenomenon that the synchronization level varies with time is robustly observed as 'chaotic itinerancy' in a model of regional business cycles where all regions are homogeneous and connected with each other through producers' expectations. Chaotic itinerancy is complex behavior in high-dimensional dynamical systems, where chaotic trajectories exhibit itinerant motion among many different ordered states.