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Periodic solutions of discrete-time Quaternion-valued BAM neural networks

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  • Li, Donghua
  • Zhang, Zhengqiu
  • Zhang, Xiaoluan

Abstract

The existence and global asymptotic stability of periodic solutions for a class of discrete-time Quaternion-valued BAM neural networks are considered. Without using the estimate priori approach of periodic solutions, the fixed point theorem and the approach of combining a continuation theorem of coincidence degree theory with a Lyapunov sequence, without decomposing the discrete-time Quaternion-valued BAM neural networks into eight real-valued differential equations, by using a continuation theorem and constructing two Lyapunov sequences, the criterion to ensure the existence of periodic solutions for the considered networks is put forward. Next, by constructing two Lyapunov sequences, a criterion assuring the global asymptotic stability of periodic solutions of the quaternion-valued neural networks is achieved. Compared with the skills and results in the existing literature, our skills and results are completely new.

Suggested Citation

  • Li, Donghua & Zhang, Zhengqiu & Zhang, Xiaoluan, 2020. "Periodic solutions of discrete-time Quaternion-valued BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920305403
    DOI: 10.1016/j.chaos.2020.110144
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    References listed on IDEAS

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    1. Tan, Manchun & Liu, Yunfeng & Xu, Desheng, 2019. "Multistability analysis of delayed quaternion-valued neural networks with nonmonotonic piecewise nonlinear activation functions," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 229-255.
    2. Shiping Shen & Bing Li & Yongkun Li, 2018. "Anti-Periodic Dynamics of Quaternion-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays on Time Scales," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-14, June.
    3. Tu, Zhengwen & Zhao, Yongxiang & Ding, Nan & Feng, Yuming & Zhang, Wei, 2019. "Stability analysis of quaternion-valued neural networks with both discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 342-353.
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    Cited by:

    1. Zhang, Hai & Chen, Xinbin & Ye, Renyu & Stamova, Ivanka & Cao, Jinde, 2023. "Adaptive quasi-synchronization analysis for Caputo delayed Cohen–Grossberg neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 49-65.
    2. Zhang, Zhengqiu & Yang, Zhen, 2023. "Asymptotic stability for quaternion-valued fuzzy BAM neural networks via integral inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Deng, Jie & Li, Hong-Li & Cao, Jinde & Hu, Cheng & Jiang, Haijun, 2023. "State estimation for discrete-time fractional-order neural networks with time-varying delays and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    4. Gao, Shang & Peng, Keyu & Zhang, Chunrui, 2021. "Existence and global exponential stability of periodic solutions for feedback control complex dynamical networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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