NONLINEAR ANALYSIS OF TIME SERIES IN COMPLEX SYSTEMS

Head: Dr. Luciano Zunino

Members and/or Collaborators:

Internal collaborators:
- BSc. Leopoldo Garavaglia
- Dr. Pedro Rueda Suescun

External collaborators:
- Dr. Cristina Masoller, Department of Physics, Universitat Politècnica de Catalunya, Barcelona, Spain.
- Dr. Haroldo V. Ribeiro, Department of Physics, Universidade Estadual de Maringá, Maringá, Brazil.
- Dr. Miguel C. Soriano, Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), Palma de Mallorca, Spain.
- Dr. Claudio Mirasso, Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), Palma de Mallorca, Spain.
- Dr. Diego Martín Mateos, Institute of Applied Mathematics of the Littoral (IMAL), Santa Fe, Argentina.
- Dr. Felipe Esteban Olivares Zamora, Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), Palma de Mallorca, Spain.
- Dr. Osvaldo Aníbal Rosso, Institute of Physics, Universidade Federal de Alagoas, Maceió, Brazil.
- Prof. Aurelio F. Bariviera, Universitat Rovira i Virgili, Department of Business, ECO-SOS, Av. Universitat 1, 43204 Reus, Spain.

Main Research Topics

  • Characterization of nonlinear dynamics in complex systems through the analysis of derived time series.
  • Development of quantifiers to improve discrimination and classification of underlying complex dynamics.
  • Implementation of proposed descriptors across diverse application fields, identifying their advantages and limitations.
  • Optimization and/or generalization of existing analysis techniques.
  • Classification of time series by combining symbolic entropy measures and machine learning techniques.
  • Identification of characteristic scales and self-similarity using ordinal patterns within a multiscale framework.
  • Quantification of heterogeneity and redundancy in multiple time series.

Brief Overview

In recent years, our research has focused on the analysis of time series derived from complex systems. The characterization of temporal fluctuations of observable quantities provides essential information for understanding the mechanisms governing the system dynamics. In this context, we have explored fractal and multifractal techniques, as well as the estimation of quantifiers derived from Information Theory (entropy measures, complexity, divergences, among others).

One of the main objectives is to distinguish between deterministic chaotic systems and purely stochastic systems. Although these systems share several properties, they exhibit fundamentally different behaviors. The ability to discriminate between them is essential for subsequent theoretical modeling.

Recent applications have incorporated techniques based on ordinal patterns. These methods are efficient and robust for analyzing large volumes of experimental data (typically non-stationary data with anomalies), in real time, and without requiring prior preprocessing. Within the current Big Data paradigm, these properties make ordinal pattern-based methods particularly attractive and motivate interdisciplinary research efforts.

Keywords: Time series – Complex systems – Nonlinear dynamics – Temporal correlations – Ordinal patterns

Recent Publications:

  • Tarozo, M. M., Pessa, A. A. B., Zunino, L., Rosso, O. A., Perc, M. & Ribeiro, H. V. Two-by-two ordinal patterns in art paintings. PNAS Nexus, Vol. 4 (3), pgaf092 (14 pages), 2025.
  • Zunino, L., Porte, X. & Soriano, M. C. Identifying ordinal similarities at different temporal scales. Entropy, Vol. 26 (12), 1016, 2024.
  • Zunino, L. Revisiting the characterization of resting brain dynamics with the permutation Jensen–Shannon distance. Entropy, Vol. 26 (5), 432, 2024.
  • Voltarelli, L. G. J. M., Pessa, A. A. B., Zunino, L., Zola, R. S., Lenzi, E. K., Perc, M. & Ribeiro, H. V. Characterizing unstructured data with nearest-neighbor permutation entropy. Chaos, Vol. 34 (5), 053130 (13 pages), 2024.

 

Research Lines: