Characterizing Nonlinear Dynamics of Logistic Map Using Machine Learning: A Coarse Approach

Abstract:

Identifying nonlinear dynamic systems that often exhibit chaotic behavior can be a complex task. Recognizing chaotic behavior in data can provide valuable insights for its utilization. Mathematically, the identification of chaotic behavior in data typically requires the consideration of multiple parameters. However, nonlinear dynamic systems can be readily identified using machine learning. In this study, a machine learning model was constructed using a deterministic dataset generated from logistic map equations, employing the Long Short-Term Memory (LSTM) architecture. The outcomes of the machine learning model take the form of data classification, distinguishing between predictable and unpredictable data with quite high validity.

• Periodical: Engineering Headway (Volume 27)
• Pages: 202-213
• DOI: https://doi.org/10.4028/p-IBM8rN
• Online since: October 2025
• Authors: Bagus Setya Aji, Fakhrudin Nugroho*, Moh Edi Wibowo
• Keywords: Chaotic Behavior, Data Classification, Long Short-Term Memory, Machine Learning, Nonlinear Dynamic

References

[1] Barrat, A., Barthelemy, M. and Vespignani, A. Dynamical Processes on Complex Networks (Cambridge University Press, New York, 2008).

[2] Flake, G. W. The Computational Beauty of Nature Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation (MIT Press, London, 2000), p.141.

[3] Baker, G. L. and Gollub, J. P., Chaotic Dynamics: An Introduction (Cambridge University Press, New York, 1990), p.76.

[4] Baptista, M. S. and Caldas, I. L. 'Dynamics of the Kicked Logistic Map', Chaos, Solitons and Fractals, 7(3), 325–336 (1996).

DOI: 10.1016/0960-0779(95)00083-6

[5] Collet, P., and Eckmann, J.-P., Iterated Mapson the Interval as Dynamical Systems (Birkha ü ser, Boston, 2009), Pp. 1-7.

[6] Gabriel, J. P., Saucy, F. and Bersier, L. F. 'Paradoxes in the logistic equation?', Ecological Modelling, 185(1), 147–151 (2005).

DOI: 10.1016/j.ecolmodel.2004.10.009

[7] Cielen, D., Meysman, A. D. B. and Ali, M. Introducing Data Science. (Manning Publications Co., New York, 2016), p.12.

[8] Mueller, J.P. and Massaron, L. Machine Learning for Dummies, (John Wiley & Sons, Inc., New Jersey, 2016) pp.219-236

[9] Roy, S., Road, B.B., Pradesh, M., & Rana, D. (n.d.). Machine Learning in Nonlinear Dynamical Systems. General Article, Springer. (2021)

[10] Boullé, N., Dallas, V., Nakatsukasa, Y., & Samaddar, D. Classification of chaotic time series with deep learning. Physica D: Nonlinear Phenomena, 403, 132261 (2020).

DOI: 10.1016/j.physd.2019.132261

[11] Monga, B., & Moehlis, J., Supervised learning algorithms for controlling underactuated dynamical systems.

[12] Physica D: Nonlinear Phenomena, 412, 132621 (2020).

[13] Ahmed, S. E., San, O., Rasheed, A., & Iliescu, T., A long short-term memory embedding for hybrid uplifted reduced order models. Physica D: Nonlinear Phenomena, 409, 132471 (2020).

DOI: 10.1016/j.physd.2020.132471

[14] May, R.M. 'Simple mathematical models with very complicated dynamics', Nature, 261(5560), 459–467, (1976).

DOI: 10.1038/261459a0

[15] Moon, F.C. Chaotic and Fractal Dynamics, SIAM Review. Weinheim: Wiley-VCH, (2004).

[16] Moysis, L. et al. 'A chaotic path planning generator based on logistic map and modulo tactics', Robotics and Autonomous Systems, 124, 103377, (2020).

DOI: 10.1016/j.robot.2019.103377

[17] Müller, A.C. and Guido, S. Introduction to Machine Learning with Python, Proceedings of the Specia lity Conference on Infrastructure Condition Assessment: Art, Science, Practice. United States: O'Reilly Media, Inc., (2017)

[18] Brownlee, J. 'Long Short-Term Memory Networks with Python', Machine Learning Mastery with Python, 1(1), 228, (2017).

[19] Rosenstein, M.T., Collins, J.J. and De Luca, C.J. 'A practical method for calculating largest Lyapunov exponents from small data sets', Physica D, 65 (1–2), 117–134. (1993)

DOI: 10.1016/0167-2789(93)90009-p