Year: 2025
Type: article
Abstract: Recurrence analysis is a powerful tool for nonlinear time series analysis deeply rooted in the theory of dynamical systems, finding applications across many areas of science. It works by mapping recurrences of a time series or phase space trajectory into a logical matrix. Recurrence quantification analyses (RQAs) are computed from its internal structures, such as recurrence density and the distribution of diagonal and vertical lines. Here, we link the density-based recurrence measures such as determinism and laminarity to the concept of microstates. We present a way to obtain the histogram of both diagonal and vertical lines from recurrence microstates, which are small square submatrices of the recurrence matrix. This approach opens up a line of research by reframing traditional RQAs in terms of microstates. Therefore, we establish a bridge between concepts of traditional lines-based RQA and recurrence microstates, and illustrate this for various paradigmatic systems.
Source: Physical review. E
Authors: Felipe Eduardo Lopes da Cruz, Thiago de Lima Prado, Sergio Roberto Lopes, Norbert Marwan, Jürgen Kurths
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4409527583