Recurrence Pattern Correlation (RPC) [1] is a novel method designed to bridge the gap between qualitative Recurrence Plot (RP) [2] inspection and traditional quantitative measures. While Recurrence Quantification Analysis (RQA) typically relies on global metrics like line-based statistics, RPC introduces a spatial-statistics-inspired approach that captures localized and system-specific structures in RPs.
Recurrence Plots (RPs) are powerful tools for visualizing the dynamics of time series. However, conventional RQA may overlook localized or scale-dependent features. RPC addresses this by measuring the correlation of an RP to patterns of arbitrary shape and scale using a spatial autocorrelation metric derived from Moran's I [3].
This approach enables the detection and quantification of long-range, structured correlations in RPs—revealing hidden dynamics such as the unstable manifolds of periodic orbits. Applications include visualizing bifurcations in the Logistic map, characterizing the mixed phase space in the Standard map, and tracking unstable periodic orbits in the Lorenz '63 system.
- ✅ Introduces a novel pattern-based quantifier inspired by Moran’s I [3]
- 📊 Captures localized and long-range temporal correlations from binary recurrence plots
- 🔍 Detects system-specific structures across arbitrary shapes and scales, which are related to combinations of the recurrence relation of distinct time lags tuples
- Visualizing unstable manifolds in nonlinear dynamical systems
- Dissecting phase space complexity in mixed or chaotic regimes
- Tracking periodic orbits and structure formation in RPs
- Augmenting traditional RQA with more flexible, pattern-sensitive analysis
[1] Marghoti, G., Silva, M. P., Prado, T. D. L., Lopes, S. R., Kurths, J., & Marwan, N. (2025). Recurrence Patterns Correlation. arXiv preprint arXiv:2508.11367. https://doi.org/10.48550/arXiv.2508.11367
[2] N. Marwan, M. C. Romano, M. Thiel, J. Kurths, Recurrence Plots for the Analysis of Complex Systems, Phys. Rep. 438 (2007) 237–329.
[3] H. Li, C. A. Calder, N. Cressie, Beyond Moran’s I: Testing for Spatial Dependence Based on the Spatial Autoregressive Model, Geogr. Anal. 39 (2007) 357–375.