Recurrence-based evolving networks for time series analysis of complex systems
R. V. Donner, J. F. Donges, Y. Zou, N. Marwan, J. Kurths
This paper presents a novel approach for analyzing the structural properties of time series from real-world complex systems by means of evolving complex networks. Starting from the concept of recurrences in phase space, the recurrence matrices corresponding to different parts of a time series are re-interpreted as the adjacency matrices of complex networks, which link different observations if the associated temporal evolution is sufficiently similar. We provide some illustrative examples demonstrating that the local properties of the resulting recurrence networks allow identifying dynamically invariant objects in the phase space of complex systems. Moreover, changes in the global network properties of evolving recurrence networks allow identifying time intervals containing hidden dynamical transitions, which is exemplified for some financial time series.