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Exponential periodicity and stability of delayed neural networks

Author

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  • Sun, Changyin
  • Feng, Chun-Bo

Abstract

In this paper, exponential periodicity and stability of delayed neural networks is investigated. Without assuming the boundedness and differentiability of the activation functions, some new sufficient conditions ensuring existence and uniqueness of periodic solution for a general class of neural systems are obtained. The delayed Hopfield network, bidirectional associative memory network, and cellular neural network are special cases of the neural system model considered.

Suggested Citation

  • Sun, Changyin & Feng, Chun-Bo, 2004. "Exponential periodicity and stability of delayed neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 469-478.
    • Handle: RePEc:eee:matcom:v:66:y:2004:i:6:p:469-478
    DOI: 10.1016/j.matcom.2004.03.001
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    Citations

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    Cited by:

    1. Zhang, Yinping, 2009. "Stationary oscillation for cellular neural networks with time delays and impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3174-3178.
    2. Zhu, Song & Shen, Yi & Chen, Guici, 2012. "Noise suppress exponential growth for hybrid Hopfield neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 86(C), pages 10-20.
    3. Zhao, Hongyong & Mao, Zisen, 2009. "Boundedness and stability of nonautonomous cellular neural networks with reaction-diffusion terms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1603-1617.
    4. Yang, Xiaofan & Liao, Xiaofeng & Megson, Graham M. & Evans, David J., 2005. "Global exponential periodicity of a class of neural networks with recent-history distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 441-447.
    5. Song, Qiankun, 2008. "Novel criteria for global exponential periodicity and stability of recurrent neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 720-728.
    6. Liu, Yiguang & You, Zhisheng, 2007. "Multi-stability and almost periodic solutions of a class of recurrent neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 554-563.
    7. Song, Qiang & Cao, Jinde & Liu, Fang, 2012. "Pinning synchronization of linearly coupled delayed neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 86(C), pages 39-51.
    8. Gui, Zhanji & Yang, Xiao-Song & Ge, Weigao, 2008. "Existence and global exponential stability of periodic solutions of recurrent cellular neural networks with impulses and delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(1), pages 14-29.

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