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Chaos control and solutions of fractional-order Malkus waterwheel model

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  • Akinlar, Mehmet Ali
  • Tchier, Fairouz
  • Inc, Mustafa

Abstract

Malkus waterwheel model is a Lorenz type chaotic-physical model expressed in terms of a system of nonlinear ordinary differential equations. In this investigation, we consider fractional-order Malkus waterwheel model via Caputo type time derivative and present chaos control, anti-synchronization, numerical solutions of the fractional system. We also associate fractional-order Malkus model with two different optimal control problems. Computational results indicate that this study may serve as a framework for chaotic behavior analysis and approximate solutions of many different parametric systems. The paper may be considered as a novel contribution because optimal control formulations, numerical solutions, stability analysis for fractional-order Malkus model are studied first time in this paper. This research work may be useful for researchers concerning with chaos analysis and approximate solutions of fractional-order chaotic dynamical systems.

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  • Akinlar, Mehmet Ali & Tchier, Fairouz & Inc, Mustafa, 2020. "Chaos control and solutions of fractional-order Malkus waterwheel model," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    • Handle: RePEc:eee:chsofr:v:135:y:2020:i:c:s096007792030148x
    DOI: 10.1016/j.chaos.2020.109746
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    References listed on IDEAS

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    4. Bayat, Alireza & Khazaei, Ehsan & Mahdavi, Sadegh, 2019. "Economic-Based Synchronization and Control of New Fractional-Order Chaotic System Based on Lyapunov Theorem," MPRA Paper 95394, University Library of Munich, Germany.
    5. Yan, Jianping & Li, Changpin, 2005. "Generalized projective synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1119-1124.
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    Cited by:

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    3. Ávalos-Ruíz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Cortes-Campos, H.M. & Lavín-Delgado, J.E., 2023. "A RGB image encryption technique using chaotic maps of fractional variable-order based on DNA encoding," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. Xin, Baogui & Peng, Wei & Kwon, Yekyung, 2020. "A discrete fractional-order Cournot duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).

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