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Stability and Synchronization of a Fractional-Order Unified System with Complex Variables

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  • Yanyun Xie
  • Wenliang Cai
  • Jing Wang
  • Jesus M. Munoz-Pacheco

Abstract

In this paper, a fractional-order unified system with complex variables is proposed. Firstly, the basic properties of the system including the equilibrium points and symmetry are analyzed. Bifurcations of the system in commensurate-order and incommensurate-order cases are studied. Tangent and period-doubling bifurcations can be observed when a derivative order or a parameter is varied. The stabilization the system is investigated via the predict feedback method. Based on the stability theory of fractional-order systems, a projective synchronization for the fractional-order unified complex system is proposed by designing an appropriate controller. Numerical simulations are applied to verify the effectiveness of the proposed scheme.

Suggested Citation

  • Yanyun Xie & Wenliang Cai & Jing Wang & Jesus M. Munoz-Pacheco, 2024. "Stability and Synchronization of a Fractional-Order Unified System with Complex Variables," Discrete Dynamics in Nature and Society, Hindawi, vol. 2024, pages 1-10, June.
    • Handle: RePEc:hin:jnddns:2728661
    DOI: 10.1155/2024/2728661
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