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Suppressing chaos in discontinuous systems of fractional order by active control

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  • Danca, Marius-F.
  • Garrappa, Roberto

Abstract

In this paper, a chaos control algorithm for a class of piece-wise continuous chaotic systems of fractional order, in the Caputo sense, is proposed. With the aid of Filippov’s convex regularization and via differential inclusions, the underlying discontinuous initial value problem is first recast in terms of a set-valued problem and hence it is continuously approximated by using Cellina’s Theorem for differential inclusions. For chaos control, an active control technique is implemented so that the unstable equilibria become stable. As example, Shimizu–Morioka’s system is considered. Numerical simulations are obtained by means of the Adams–Bashforth–Moulton method for differential equations of fractional-order.

Suggested Citation

  • Danca, Marius-F. & Garrappa, Roberto, 2015. "Suppressing chaos in discontinuous systems of fractional order by active control," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 89-102.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:89-102
    DOI: 10.1016/j.amc.2014.10.133
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    Cited by:

    1. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong, 2019. "Chaotic analysis and adaptive synchronization for a class of fractional order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 33-42.
    2. Chakraborty, Arkaprovo & Veeresha, P., 2024. "Investigating the dynamics, synchronization and control of chaos within a transformed fractional Samardzija–Greller framework," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
    4. Jose-Cruz Nuñez-Perez & Vincent-Ademola Adeyemi & Yuma Sandoval-Ibarra & Francisco-Javier Perez-Pinal & Esteban Tlelo-Cuautle, 2021. "Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms," Mathematics, MDPI, vol. 9(11), pages 1-22, May.

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