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Delayed control-based controllability of discrete fractional higher-order neural networks

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  • Ma, Weiyuan
  • Ma, Chenjun
  • Wang, Xiaoqin
  • Sun, Weigang

Abstract

This paper focuses on the controllability issues of discrete fractional higher-order neural networks with delayed control mechanisms. The matrix representation of the discrete Mittag-Leffler function is defined, and several fundamental properties are established using the discrete Laplace transform. It is revealed that the discrete fractional linear system is controllable if and only if the controllability Gramian matrix is nonsingular. Building on this foundation, a delayed control scheme is developed for discrete fractional higher-order neural networks, employing Schauder’s Fixed Point Theorem alongside the Gramian matrix. Finally, the effectiveness and practicality of the proposed methodologies are validated through three illustrative examples.

Suggested Citation

  • Ma, Weiyuan & Ma, Chenjun & Wang, Xiaoqin & Sun, Weigang, 2025. "Delayed control-based controllability of discrete fractional higher-order neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p1:s0960077925009464
    DOI: 10.1016/j.chaos.2025.116933
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    References listed on IDEAS

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    1. Ma, Weiyuan & Bao, Xionggai & Ma, Chenjun, 2024. "Controllability of higher-order networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 653(C).
    2. Hai Zhang & Jinde Cao & Wei Jiang, 2013. "Reachability and Controllability of Fractional Singular Dynamical Systems with Control Delay," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, November.
    3. Hai Zhang & Jinde Cao & Wei Jiang, 2013. "Reachability and Controllability of Fractional Singular Dynamical Systems with Control Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Khennaoui, Amina-Aicha & Ouannas, Adel & Bendoukha, Samir & Grassi, Giuseppe & Lozi, René Pierre & Pham, Viet-Thanh, 2019. "On fractional–order discrete–time systems: Chaos, stabilization and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 150-162.
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