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

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

Discrete Dynamics in Nature and Society, 2024, vol. 2024, 1-10

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.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:2728661

DOI: 10.1155/2024/2728661

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