Transformada wavelet en el análisis de series de tiempo caóticas
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ene 8, 2026
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https://doi.org/10.36677/rici.v4i1.26712
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Eduardo Jiménez-López
http://orcid.org/0000-0002-1883-3890
Nely Plata-Cesar
http://orcid.org/0000-0002-3643-130X
http://orcid.org/0000-0002-1883-3890
Nely Plata-Cesar
http://orcid.org/0000-0002-3643-130X
Resumen
En este escrito se realiza la evaluación de un sistema caótico con múltiples atractores a través del análisis de series temporales con la transformada Wavelet. Esta técnica permite analizar las fluctuaciones de tiempo-frecuencia en diferentes resoluciones, permitiendo identificar patrones complejos y transitorios en las series de tiempo caóticas. Con la transformada Wavelet se realiza la representación visual de las potencias más elevadas de una dinámica caótica que puede facilitar el entendimiento del sistema respecto a cómo evoluciona a lo largo del tiempo y en distintas escalas. Además, identifica patrones transitorios, detecta eventos o cambios en la serie de tiempo, lo que es útil para identificar las condiciones de transición de un estado caótico. Por lo tanto, la descomposición multiresolución de la transformada wavelet ayuda a mejorar la exactitud de los modelos predictivos de series temporales que incluyen una dinámica caótica.
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Como citar
JIMÉNEZ-LÓPEZ, Eduardo; PLATA-CESAR, Nely.
Transformada wavelet en el análisis de series de tiempo caóticas.
Ideas en Ciencias de la Ingeniería, [S.l.], v. 4, n. 1, p. 79-95, ene. 2026.
ISSN 2992-7447.
Disponible en: <https://ideasencienciasingenieria.uaemex.mx/article/view/26712>. Fecha de acceso: 26 ago. 2026
doi: https://doi.org/10.36677/rici.v4i1.26712.
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Esta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial-SinObrasDerivadas 4.0.
Citas
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[3] Mashuri, A., Adenan, N. H., Abd Karim, N. S., Tho, S. W., & Zeng, Z. (2024). Application of chaos theory in different fields-a literature review. Journal of Science and Mathematics Letters, 12(1), 92-101. DOI: https://doi.org/10.37134/jsml.vol12.1.11.2024
[4] Szczęsna, A., Augustyn, D. R., Josiński, H., Harężlak, K., Świtoński, A., & Kasprowski, P. (2023). Chaotic biomedical time signal analysis via wavelet scattering transform. Journal of Computational Science, 72, 102080. DOI: https://doi.org/10.1016/j.jocs.2023.102080
[5] Tian, Z. (2023). Analysis and research on chaotic dynamics behaviour of wind power time series at different time scales. Journal of Ambient Intelligence and Humanized Computing, 14(2), 897-921. DOI: https://doi.org/10.1007/s12652-021-03343-1
[6] Hu, J., Hu, Y., Chen, W., Jin, M., Pan, S., Wen, Q., & Liang, Y. (2024). Attractor memory for long-term time series forecasting: A chaos perspective. arXiv preprint arXiv:2402.11463. DOI:
https://doi.org/10.48550/arXiv.2402.11463
[7] Li, P. C., Zhang, F., Gao, L., Liu, Y. Q., & Ren, X. Y. (2021). A novel model for chaotic complex time series with large of data forecasting. Knowledge-Based Systems, 222, 107009. DOI: https://doi.org/10.1016/j.knosys.2021.107009
[8] Arts, L. P., & Van den Broek, E. L. (2022). The fast continuous wavelet transformation (fCWT) for real-time, high-quality, noise-resistant time–frequency analysis. Nature Computational Science, 2(1), 47-58. DOI: https://doi.org/10.1038/s43588-021-00183-z
[9] Guo, T., Zhang, T., Lim, E., Lopez-Benitez, M., Ma, F., & Yu, L. (2022). A review of wavelet analysis and its applications: Challenges and opportunities. IEEe Access, 10, 58869-58903. DOI: 10.1109/ACCESS.2022.3179517
[10] Kumar, A., Tomar, H., Mehla, V. K., Komaragiri, R., & Kumar, M. (2021). Stationary wavelet transform based ECG signal denoising method. ISA transactions, 114, 251-262. DOI: https://doi.org/10.1016/j.isatra.2020.12.029
[11] Vaidyanathan, P. P., & Djokovic, I. (2022). Wavelet transforms. In Mathematics for Circuits and Filters (pp. 131-216). CRC Press.
[12] Koverda, V. P., & Skokov, V. N. (2023). Random process with a turbulent power spectrum. Physica A: Statistical Mechanics and its Applications, 612, 128491. DOI: https://doi.org/10.1016/j.physa.2023.128491
[13] Wu, Y., Wang, C., & Deng, Q. (2021). A new 3D multi-scroll chaotic system generated with three types of hidden attractors. The European Physical Journal Special Topics, 230(7), 1863-1871. DOI: https://doi.org/10.1140/epjs/s11734-021-00119-8
[14] Yang, Y., Huang, L., Kuznetsov, N. V., & Lai, Q. (2023). Design and implementation of grid-wing hidden chaotic attractors with only stable equilibria. IEEE Transactions on Circuits and Systems I: Regular Papers, 70(12), 5408-5420. DOI: https://doi.org/10.1109/TCSI.2023.3312489
[15] Li, F., & Zeng, J. (2023). Multi-scroll attractor and multi-stable dynamics of a three-dimensional jerk system. Energies, 16(5), 2494. DOI: 10.3390/en16052494
[16] Li, C., Hu, W., Sprott, J. C., & Wang, X. (2015). Multistability in symmetric chaotic systems. The European Physical Journal Special Topics, 224(8), 1493-1506. DOI: https://doi.org/10.1140/epjst/e2015-02475-x