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Synchronization of chaotic neural networks via output or state coupling

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  • Lu, Hongtao
  • van Leeuwen, C.

Abstract

We consider the problem of global exponential synchronization between two identical chaotic neural networks that are linearly and unidirectionally coupled. We formulate a general framework for the synchronization problem in which one chaotic neural network, working as the driving system (or master), sends its output or state values to the other, which serves as the response system (or slave). We use Lyapunov functions to establish general theoretical conditions for designing the coupling matrix. Neither symmetry nor negative (positive) definiteness of the coupling matrix are required; under less restrictive conditions, the two coupled chaotic neural networks can achieve global exponential synchronization regardless of their initial states. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Suggested Citation

  • Lu, Hongtao & van Leeuwen, C., 2006. "Synchronization of chaotic neural networks via output or state coupling," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 166-176.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:1:p:166-176
    DOI: 10.1016/j.chaos.2005.08.175
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    1. P. N. Steinmetz & A. Roy & P. J. Fitzgerald & S. S. Hsiao & K. O. Johnson & E. Niebur, 2000. "Attention modulates synchronized neuronal firing in primate somatosensory cortex," Nature, Nature, vol. 404(6774), pages 187-190, March.
    2. Cheng, Chao-Jung & Liao, Teh-Lu & Hwang, Chi-Chuan, 2005. "Exponential synchronization of a class of chaotic neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 197-206.
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    Cited by:

    1. Su, Haipeng & Luo, Runzi & Huang, Meichun & Fu, Jiaojiao, 2022. "Practical fixed time active control scheme for synchronization of a class of chaotic neural systems with external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Cui, Baotong & Lou, Xuyang, 2009. "Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 288-294.
    3. Sun, Li & Wang, Jiang & Deng, Bin, 2009. "Global synchronization of two Ghostburster neurons via active control," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1213-1220.
    4. Sheng, Li & Yang, Huizhong & Lou, Xuyang, 2009. "Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 930-939.
    5. Karimi, Hamid Reza & Maass, Peter, 2009. "Delay-range-dependent exponential H∞ synchronization of a class of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1125-1135.

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