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A new approach to extreme event prediction and mitigation via Markov-model-based chaos control

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  • Kaveh, Hojjat
  • Salarieh, Hassan

Abstract

Despite that the border between chaotic and stochastic systems is exactly defined, scientists, use high dimensional chaotic dynamics to model numerous stochastic models and sometimes use stochastic models to study chaotic systems. In this paper, we have investigated chaotic systems with a stochastic approach and proposed an estimator for the chaotic system which is used to present different algorithms for chaos control, extreme event prediction and extreme event mitigation. The stochastic estimator is constructed by meshing the phase space and applying the cell mapping method (with some considerations) which provides us with a model-free approximation of the systems. The algorithms are ideal for real-world applications where there are some noises and the model of the system is unknown. Besides, the proposed methods are adopted for when the control signal is limited to a few specific values. We have tested these algorithms on Logistic, Henon and a physiological control system.

Suggested Citation

  • Kaveh, Hojjat & Salarieh, Hassan, 2020. "A new approach to extreme event prediction and mitigation via Markov-model-based chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302277
    DOI: 10.1016/j.chaos.2020.109827
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    References listed on IDEAS

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    1. Wang, Biao & Mao, Zhizhong & Huang, Keke, 2019. "Detecting outliers for complex nonlinear systems with dynamic ensemble learning," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 98-107.
    2. Santos, Moises S. & Szezech, José D. & Batista, Antonio M. & Iarosz, Kelly C. & Caldas, Iberê L. & Viana, Ricardo L., 2019. "Dragon-kings death in nonlinear wave interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    3. Kaveh, H. & Salarieh, H. & Hajiloo, R., 2018. "On the control of unknown continuous time chaotic systems by applying Takens embedding theory," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 53-57.
    4. Mattheakis, M. & Pitsios, I.J. & Tsironis, G.P. & Tzortzakis, S., 2016. "Extreme events in complex linear and nonlinear photonic media," Chaos, Solitons & Fractals, Elsevier, vol. 84(C), pages 73-80.
    5. Shirkavand, Mehrdad & Pourgholi, Mahdi, 2018. "Robust fixed-time synchronization of fractional order chaotic using free chattering nonsingular adaptive fractional sliding mode controller design," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 135-147.
    6. Jokar, Meysam & Salarieh, Hassan & Alasty, Aria, 2019. "On the existence of proper stochastic Markov models for statistical reconstruction and prediction of chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 373-382.
    7. Li, Li, 2015. "Bifurcation and chaos in a discrete physiological control system," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 397-404.
    8. Sinha, Amit & Horvath, Philip A. & Beason, Tyler & Roos, Kelly R., 2019. "Simulation of a financial market: The possibility of catastrophic disequilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 13-16.
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    Cited by:

    1. Lopes, António M. & Machado, J.A. Tenreiro, 2022. "Multidimensional scaling and visualization of patterns in global large-scale accidents," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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