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A novel criterion for global asymptotic stability of BAM neural networks with time delays

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  • Park, Ju H.

Abstract

A delay-differential equation modelling a bidirectional associative memory (BAM) neural networks is investigated. An asymptotic stability of the BAM neural networks with time delays is considered by constructing a new suitable Lyapunov functional and some matrix inequality technique. A novel delay-dependent stability criterion is given in terms of matrix inequalities, which can be solved easily by various optimization algorithms.

Suggested Citation

  • Park, Ju H., 2006. "A novel criterion for global asymptotic stability of BAM neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 446-453.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:2:p:446-453
    DOI: 10.1016/j.chaos.2005.08.018
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    1. Huang, Xia & Cao, Jinde & Huang, De-Shuang, 2005. "LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 885-898.
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    Cited by:

    1. Qian-hong Zhang & Li-hui Yang, 2012. "Dynamical analysis of fuzzy BAM neural networks with variable delays," Fuzzy Information and Engineering, Springer, vol. 4(1), pages 93-104, March.
    2. Zheng, Baodong & Zhang, Yazhuo & Zhang, Chunrui, 2008. "Global existence of periodic solutions on a simplified BAM neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1397-1408.
    3. Singh, Vimal, 2009. "Remarks on estimating upper limit of norm of delayed connection weight matrix in the study of global robust stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2013-2017.
    4. Mathiyalagan, K. & Park, Ju H. & Sakthivel, R., 2015. "Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 967-979.
    5. R. Sakthivel & R. Raja & S. M. Anthoni, 2011. "Exponential Stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 166-187, July.
    6. Ratnavelu, K. & Manikandan, M. & Balasubramaniam, P., 2015. "Synchronization of fuzzy bidirectional associative memory neural networks with various time delays," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 582-605.
    7. Park, Ju H., 2008. "On global stability criterion of neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 444-449.
    8. Singh, Vimal, 2009. "Novel global robust stability criterion for neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 348-353.
    9. R. Sakthivel & R. Raja & S. M. Anthoni, 2013. "Exponential Stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 251-273, July.
    10. Zhang, Jianmei & Wu, Jianwei & Bao, Haibo & Cao, Jinde, 2018. "Synchronization analysis of fractional-order three-neuron BAM neural networks with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 441-450.
    11. 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.
    12. Hien, Le Van & Son, Doan Thai, 2015. "Finite-time stability of a class of non-autonomous neural networks with heterogeneous proportional delays," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 14-23.
    13. Song, Qiankun & Wang, Zidong, 2008. "Neural networks with discrete and distributed time-varying delays: A general stability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1538-1547.
    14. Singh, Vimal, 2007. "Novel LMI condition for global robust stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 503-508.
    15. J. H. Park & S. M. Lee & H. Y. Jung, 2009. "LMI Optimization Approach to Synchronization of Stochastic Delayed Discrete-Time Complex Networks," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 357-367, November.
    16. Yang, Yu & Ye, Jin, 2009. "Stability and bifurcation in a simplified five-neuron BAM neural network with delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2357-2363.
    17. Sader, Malika & Abdurahman, Abdujelil & Jiang, Haijun, 2018. "General decay synchronization of delayed BAM neural networks via nonlinear feedback control," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 302-314.
    18. Liao, Huaying & Zhang, Zhengqiu & Ren, Ling & Peng, Wenli, 2017. "Global asymptotic stability of periodic solutions for inertial delayed BAM neural networks via novel computing method of degree and inequality techniques," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 785-797.
    19. Park, Ju H. & Lee, S.M. & Kwon, O.M., 2009. "On exponential stability of bidirectional associative memory neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1083-1091.
    20. Zhang, Qianhong & Luo, Wei, 2009. "Global exponential stability of fuzzy BAM neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2239-2245.
    21. Park, Ju H. & Kwon, O.M., 2009. "Global stability for neural networks of neutral-type with interval time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1174-1181.
    22. Wang, Huiwei & Song, Qiankun & Duan, Chengjun, 2010. "LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 837-850.
    23. Dong, Ying & Sun, Chengjun, 2009. "Global existence of periodic solutions in a special neural network model with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2249-2257.
    24. Yang, Degang & Hu, Chunyan & Chen, Yong & Wei, Pengcheng & Yang, Huaqian, 2009. "New delay-dependent global asymptotic stability criteria of delayed BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 854-864.

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