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Synchronization of fuzzy bidirectional associative memory neural networks with various time delays

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  • Ratnavelu, K.
  • Manikandan, M.
  • Balasubramaniam, P.

Abstract

The problem of synchronization for fuzzy bidirectional associative memory (BAM) neural networks (NNs) with various time delays is formulated and investigated. The various delays consist of discrete delays, unbounded distributed delays and constant delay in the leakage term (i.e. ‘leakage delay’) are considered. Then, some sufficient conditions are presented to guarantee the global asymptotic stability of the error dynamical system by using Lyapunov–Krasovskii functional and linear matrix inequality (LMI) method. As a result, we achieved synchronization of master-slave (drive-response) fuzzy BAM NNs systems. Even, if there is no leakage delay, the obtained results are less restrictive to some known sufficient conditions. Moreover, the proposed results do not require the boundedness, differentiability and monotonicity of the activation functions, which can also be easily checked via the LMI solver in robust control toolbox in Matlab. Furthermore, using a parameter-dependent Lyapunov function approach the synchronization problem for polytopic uncertain fuzzy BAM NNs with various time delays is considered. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. Finally, two numerical examples and simulations are given to illustrate the effectiveness of the derived theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:582-605
    DOI: 10.1016/j.amc.2015.07.061
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    References listed on IDEAS

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    1. 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.
    2. Yu, Juan & Hu, Cheng & Jiang, Haijun & Teng, Zhidong, 2012. "Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 895-908.
    3. Kalpana, M. & Balasubramaniam, P. & Ratnavelu, K., 2015. "Direct delay decomposition approach to synchronization of chaotic fuzzy cellular neural networks with discrete, unbounded distributed delays and Markovian jumping parameters," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 291-304.
    4. 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.
    5. Park, Ju H., 2006. "On global stability criterion for neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 897-902.
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    Cited by:

    1. Huang, Chengdai & Meng, Yijie & Cao, Jinde & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "New bifurcation results for fractional BAM neural network with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 31-44.
    2. Tu, Zhengwen & Ding, Nan & Li, Liangliang & Feng, Yuming & Zou, Limin & Zhang, Wei, 2017. "Adaptive synchronization of memristive neural networks with time-varying delays and reaction–diffusion term," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 118-128.
    3. Zhang, Guodong & Cao, Jinde, 2023. "New results on fixed/predefined-time synchronization of delayed fuzzy inertial discontinuous neural networks: Non-reduced order approach," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    4. Xie, Wenqian & Zhu, Hong & Zhong, Shouming & Zhang, Dian & Shi, Kaibo & Cheng, Jun, 2018. "Extended dissipative estimator design for uncertain switched delayed neural networks via a novel triple integral inequality," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 82-102.
    5. Xu, Liguang & Chu, Xiaoyan & Hu, Hongxiao, 2021. "Quasi-synchronization analysis for fractional-order delayed complex dynamical networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 594-613.
    6. Chengqiang Wang & Xiangqing Zhao & Can Wang & Zhiwei Lv, 2023. "Synchronization of Takagi–Sugeno Fuzzy Time-Delayed Stochastic Bidirectional Associative Memory Neural Networks Driven by Brownian Motion in Pre-Assigned Settling Time," Mathematics, MDPI, vol. 11(17), pages 1-32, August.

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