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Almost Anti-Periodic Oscillation Excited by External Inputs and Synchronization of Clifford-Valued Recurrent Neural Networks

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Listed:
  • Weiwei Qi

    (Department of Mathematics, Yunnan University, Kunming 650091, China)

  • Yongkun Li

    (Department of Mathematics, Yunnan University, Kunming 650091, China)

Abstract

The main purpose of this paper was to study the almost anti-periodic oscillation caused by external inputs and the global exponential synchronization of Clifford-valued recurrent neural networks with mixed delays. Since the space consists of almost anti-periodic functions has no vector space structure, firstly, we prove that the network under consideration possesses a unique bounded continuous solution by using the contraction fixed point theorem. Then, by using the inequality technique, it was proved that the unique bounded continuous solution is also an almost anti-periodic solution. Secondly, taking the neural network that was considered as the driving system, introducing the corresponding response system and designing the appropriate controller, some sufficient conditions for the global exponential synchronization of the driving-response system were obtained by employing the inequality technique. When the system we consider degenerated into a real-valued system, our results were considered new. Finally, the validity of the results was verified using a numerical example.

Suggested Citation

  • Weiwei Qi & Yongkun Li, 2022. "Almost Anti-Periodic Oscillation Excited by External Inputs and Synchronization of Clifford-Valued Recurrent Neural Networks," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2764-:d:879906
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    References listed on IDEAS

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    1. Rajchakit, G. & Sriraman, R. & Vignesh, P. & Lim, C.P., 2021. "Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    2. Grienggrai Rajchakit & Ramalingam Sriraman & Chee Peng Lim & Panu Sam-ang & Porpattama Hammachukiattikul, 2021. "Synchronization in Finite-Time Analysis of Clifford-Valued Neural Networks with Finite-Time Distributed Delays," Mathematics, MDPI, vol. 9(11), pages 1-18, May.
    3. Arbi, Adnène, 2021. "Novel traveling waves solutions for nonlinear delayed dynamical neural networks with leakage term," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Rajchakit, G. & Sriraman, R. & Lim, C.P. & Unyong, B., 2022. "Existence, uniqueness and global stability of Clifford-valued neutral-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 508-527.
    5. Li, Yongkun & Wang, Xiaohui, 2021. "Almost periodic solutions in distribution of Clifford-valued stochastic recurrent neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
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