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Multistability of complex-valued neural networks with time-varying delays

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  • Chen, Xiaofeng
  • Zhao, Zhenjiang
  • Song, Qiankun
  • Hu, Jin

Abstract

In this paper, the multistability problem is studied for an n-dimensional delayed complex-valued neural networks with two general classes of activation functions. After splitting the state space to multiple subsets, based on the fixed point theorem, it is shown that such complex-valued neural networks can have 9n equilibria, each of which is located in one of the subsets. Furthermore, some sufficient conditions are derived for the local exponential stability of some equilibria by employing the property of activation functions and inequality technique. As an application of these results, some criteria are obtained for checking the coexistence and exponential stability of multiple equilibria of real-valued neural networks. Two examples are performed to illustrate and validate the theoretical findings.

Suggested Citation

  • Chen, Xiaofeng & Zhao, Zhenjiang & Song, Qiankun & Hu, Jin, 2017. "Multistability of complex-valued neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 18-35.
    • Handle: RePEc:eee:apmaco:v:294:y:2017:i:c:p:18-35
    DOI: 10.1016/j.amc.2016.08.054
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    References listed on IDEAS

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    Cited by:

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    7. Liu, Yunfeng & Song, Zhiqiang & Tan, Manchun, 2019. "Multiple μ-stability and multiperiodicity of delayed memristor-based fuzzy cellular neural networks with nonmonotonic activation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 1-17.
    8. Yu, Siyi & Li, Hua & Chen, Xiaofeng & Lin, Dongyuan, 2023. "Multistability analysis of quaternion-valued neural networks with cosine activation functions," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    9. Xiaohui Xu & Huanbin Xue & Yiqiang Peng & Quan Xu & Jibin Yang, 2018. "Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    10. Nie, Xiaobing & Liang, Jinling & Cao, Jinde, 2019. "Multistability analysis of competitive neural networks with Gaussian-wavelet-type activation functions and unbounded time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 449-468.
    11. Xiaohui Xu & Jibin Yang & Yanhai Xu, 2019. "Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays," Complexity, Hindawi, vol. 2019, pages 1-20, June.
    12. Jin-dong Li & Nan-jing Huang, 2018. "Asymptotical Stability for a Class of Complex-Valued Projective Neural Network," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 261-270, April.
    13. Xu, Wei & Zhu, Song & Fang, Xiaoyu & Wang, Wei, 2019. "Adaptive anti-synchronization of memristor-based complex-valued neural networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    14. 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.
    15. Wu, H.G. & Ye, Y. & Bao, B.C. & Chen, M. & Xu, Q., 2019. "Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 178-185.
    16. Xiaohui Xu & Huanbin Xue & Yiqiang Peng & Jiye Zhang, 2018. "Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays," Complexity, Hindawi, vol. 2018, pages 1-16, September.
    17. Zhang, Yunzhen & Liu, Zhong & Wu, Huagan & Chen, Shengyao & Bao, Bocheng, 2019. "Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 354-363.
    18. Sriraman, R. & Cao, Yang & Samidurai, R., 2020. "Global asymptotic stability of stochastic complex-valued neural networks with probabilistic time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 103-118.
    19. Tang, Qian & Jian, Jigui, 2019. "Global exponential convergence for impulsive inertial complex-valued neural networks with time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 39-56.
    20. Kumar, Ankit & Das, Subir & Singh, Sunny & Rajeev,, 2023. "Quasi-projective synchronization of inertial complex-valued recurrent neural networks with mixed time-varying delay and mismatched parameters," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    21. Wang, Pengfei & Zou, Wenqing & Su, Huan, 2019. "Stability of complex-valued impulsive stochastic functional differential equations on networks with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 338-354.
    22. Cao, Yang & Sriraman, R. & Shyamsundarraj, N. & Samidurai, R., 2020. "Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 207-220.

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