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Global asymptotic stability of periodic solutions for inertial delayed BAM neural networks via novel computing method of degree and inequality techniques

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  • Liao, Huaying
  • Zhang, Zhengqiu
  • Ren, Ling
  • Peng, Wenli

Abstract

Firstly, by combining Mawhin’s continuation theorem of coincidence degree theory with Lyapunov functional method and by using inequality techniques, a sufficient condition on the existence of periodic solutions for inertial BAM neural networks is obtained. Secondly, a novel sufficient condition which can ensure the global asymptotic stability of periodic solutions of the system is obtained by using Lyapunov functional method and by using inequality techniques. In our paper, the assumption for boundedness on the activation functions in existing paper is removed, the conditions in inequality form in existing papers are replaced with novel conditions, and the prior estimate method of periodic solutions is replaced with Lyapunov functional method. Hence, our result on global asymptotic stability of periodic solutions for above system is less conservative than those obtained in existing paper and more novel than those obtained in existing papers.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:785-797
    DOI: 10.1016/j.chaos.2017.09.035
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    References listed on IDEAS

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    1. 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.
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    3. 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.
    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. Cui, Bao Tong & Lou, Xu Yang, 2006. "Global asymptotic stability of BAM neural networks with distributed delays and reaction–diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1347-1354.
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    Cited by:

    1. Han, Siyu & Hu, Cheng & Yu, Juan & Jiang, Haijun & Wen, Shiping, 2021. "Stabilization of inertial Cohen-Grossberg neural networks with generalized delays: A direct analysis approach," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Liu, Jin & Jian, Jigui & Wang, Baoxian, 2020. "Stability analysis for BAM quaternion-valued inertial neural networks with time delay via nonlinear measure approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 134-152.

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