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Modeling Nonlinear Dynamics and Chaos: A Review

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  • Luis A. Aguirre
  • Christophe Letellier

Abstract

This paper reviews the major developments of modeling techniques applied to nonlinear dynamics and chaos. Model representations, parameter estimation techniques, data requirements, and model validation are some of the key topics that are covered in this paper, which surveys slightly over two decades since the pioneering papers on the subject appeared in the literature.

Suggested Citation

  • Luis A. Aguirre & Christophe Letellier, 2009. "Modeling Nonlinear Dynamics and Chaos: A Review," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-35, June.
    • Handle: RePEc:hin:jnlmpe:238960
    DOI: 10.1155/2009/238960
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    Cited by:

    1. Mangiarotti, Sylvain & Le Jean, Flavie & Huc, Mireille & Letellier, Christophe, 2016. "Global modeling of aggregated and associated chaotic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 82-96.
    2. Sysoeva, Marina V. & Sysoev, Ilya V. & Prokhorov, Mikhail D. & Ponomarenko, Vladimir I. & Bezruchko, Boris P., 2021. "Reconstruction of coupling structure in network of neuron-like oscillators based on a phase-locked loop," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Aguirre, Luis A. & Letellier, Christophe, 2016. "Controllability and synchronizability: Are they related?," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 242-251.
    4. Mohammed A. El-Shorbagy & Fatma M. Al-Drees, 2023. "Studying the Effect of Introducing Chaotic Search on Improving the Performance of the Sine Cosine Algorithm to Solve Optimization Problems and Nonlinear System of Equations," Mathematics, MDPI, vol. 11(5), pages 1-25, March.
    5. Tuttle, Jacob F. & Blackburn, Landen D. & Andersson, Klas & Powell, Kody M., 2021. "A systematic comparison of machine learning methods for modeling of dynamic processes applied to combustion emission rate modeling," Applied Energy, Elsevier, vol. 292(C).
    6. Kück, Mirko & Freitag, Michael, 2021. "Forecasting of customer demands for production planning by local k-nearest neighbor models," International Journal of Production Economics, Elsevier, vol. 231(C).
    7. Artur Karimov & Erivelton G. Nepomuceno & Aleksandra Tutueva & Denis Butusov, 2020. "Algebraic Method for the Reconstruction of Partially Observed Nonlinear Systems Using Differential and Integral Embedding," Mathematics, MDPI, vol. 8(2), pages 1-22, February.

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