Time series synchronization in cross-recurrence networks: uncovering a homomorphic law across diverse complex systems

Abstract

Exploring the synchronicity between time series, especially the similar patterns during extreme events, has been a focal point of research in academia. This is due to the fact that such special dependence occurring between pairs of time series often plays a crucial role in triggering emergent behaviors in the underlying systems and is closely related to systemic risks. In this paper, we investigate the relationship between the synchronicity of time series and the corresponding topological properties of the cross-recurrence network. We discover a positive linear relationship between the probability of pairwise time series event synchronicity and the corresponding cross-recurrence network's clustering coefficient. We first provide theoretical proof, then demonstrate this relationship through simulation experiments by coupled map lattices. Finally, we empirically analyze three instances from financial systems, Earth's ecological systems, and human interactive behavioral systems to validate that this regularity is a homomorphic law in different complex systems. The discovered regularity holds significant potential for applications in monitoring financial system risks, extreme weather events, and more.