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Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays

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  • Babu, N. Ramesh
  • Balasubramaniam, P.

Abstract

In this paper, a new fractional differentiation operator is considered the convolution of a power law with a fractal derivative. The novel operator sought to attract more non-local memory effects and self-similarities in chaotic attractors. This paper addresses the problem of fractal-fractional order quaternion-valued neural networks (FFoQVNNs) with time-varying delays. The sufficient conditions for the existence and uniqueness of an equilibrium point are derived for the proposed model by employing contraction mapping. The Lyapunov direct technique and fractal-fractional differential theory achieve the finite-time synchronization criteria by dividing the FFoQVNNs into four real-valued systems. Furthermore, the settling time is determined, which impact by the fractal dimension β, fractional-order α, and control parameters. Finally, a corresponding numerical simulation is demonstrated to show the accuracy of the theoretical results.

Suggested Citation

  • Babu, N. Ramesh & Balasubramaniam, P., 2022. "Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006889
    DOI: 10.1016/j.chaos.2022.112478
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    References listed on IDEAS

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    Cited by:

    1. Admon, Mohd Rashid & Senu, Norazak & Ahmadian, Ali & Majid, Zanariah Abdul & Salahshour, Soheil, 2024. "A new modern scheme for solving fractal–fractional differential equations based on deep feedforward neural network with multiple hidden layer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 311-333.
    2. Yang, Dongsheng & Yu, Yongguang & Wang, Hu & Ren, Guojian & Zhang, Xiaoli, 2024. "Successive lag synchronization of heterogeneous distributed-order coupled neural networks with unbounded delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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