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Multistability of equilibria for Clifford-valued Cohen–Grossberg neural networks with discontinuous activation functions and time delays

Author

Listed:
  • Yang, Qiuyan
  • Qiao, Yuanhua
  • Duan, Lijuan
  • Miao, Jun

Abstract

In this paper, the multistability of Clifford-valued Cohen–Grossberg neural networks(CGNNs) model with time-varying delays and discontinuous activation function is investigated. Firstly, the existence of equilibrium points is explored, and it is found that there exist ∏A(4KA+1)n equilibrium points by deriving some sufficient conditions and Intermediate Value Theorem, and then the positive invariant is given. Next, we investigate the local stability of those multiple equilibrium points (EPs), which shows that there are ∏A(2KA+1)n locally asymptotically stable equilibrium points. Moreover, the attraction basins of the stable EPs in CGNNs are estimated and enlarged. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results.

Suggested Citation

  • Yang, Qiuyan & Qiao, Yuanhua & Duan, Lijuan & Miao, Jun, 2026. "Multistability of equilibria for Clifford-valued Cohen–Grossberg neural networks with discontinuous activation functions and time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 245(C), pages 428-446.
    • Handle: RePEc:eee:matcom:v:245:y:2026:i:c:p:428-446
    DOI: 10.1016/j.matcom.2025.12.015
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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. Liu, Yang & Wang, Zhen & Huang, Xia, 2022. "Multistability analysis of state-dependent switched Hopfield neural networks with the Gaussian-wavelet-type activation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 232-250.
    3. 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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