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On boundedness and projective synchronization of distributed order neural networks

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  • Mahmoud, Gamal M.
  • Aboelenen, Tarek
  • Abed-Elhameed, Tarek M.
  • Farghaly, Ahmed A.

Abstract

In this work, we introduced the distributed-order neural networks (DONNs) which are the generalization of integer and fractional orders neural networks. We presented and proved two theorems for bounded solutions and solutions that approach zero of these networks. The Gronwall–Bellman lemma, the asymptotical expansion of the generalized Mittag–Leffler function and Laplace transform are used to prove these theorems. We derived analytically the condition under which the solution of this network (DONN) is bounded. The active control and Lyapunov direct methods are applied to study the projective synchronization between two different chaotic DONNs. The analytical control functions are derived to achieve our synchronization. Two different examples of DONNs are given to test the validity of the analytical results of our theorems. The projective synchronization is investigated. Numerical simulations are implemented to show the agreement between both analytical and numerical results.

Suggested Citation

  • Mahmoud, Gamal M. & Aboelenen, Tarek & Abed-Elhameed, Tarek M. & Farghaly, Ahmed A., 2021. "On boundedness and projective synchronization of distributed order neural networks," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    • Handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321002885
    DOI: 10.1016/j.amc.2021.126198
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    References listed on IDEAS

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    1. Junhai Luo & Guanjun Li & Heng Liu, 2014. "Linear Control of Fractional-Order Financial Chaotic Systems with Input Saturation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, August.
    2. Guo-Hui, Li, 2005. "Synchronization and anti-synchronization of Colpitts oscillators using active control," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 87-93.
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    Cited by:

    1. Yang, Dongsheng & Wang, Hu & Ren, Guojian & Yu, Yongguang & Xu, Weiyi, 2024. "Successive lag synchronization of distributed-order multilayer neural networks with the short-term memory property," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    2. Ali, Hegagi Mohamed & Ameen, Ismail Gad & Gaber, Yasmeen Ahmed, 2024. "The effect of curative and preventive optimal control measures on a fractional order plant disease model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 496-515.
    3. Abed-Elhameed, Tarek M. & Mahmoud, Gamal M. & Elbadry, Motaz M. & Ahmed, Mansour E., 2023. "Nonlinear distributed-order models: Adaptive synchronization, image encryption and circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. 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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