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Global Lagrange stability for neutral-type Cohen–Grossberg BAM neural networks with mixed time-varying delays

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  • Jian, Jigui
  • Wang, Baoxian

Abstract

The paper discusses global Lagrange stability for a class of Cohen–Grossberg BAM neural networks of neutral-type with multiple time-varying and finite distributed delays by constructing appropriate Lyapunov-like functions. To this end, we first establish a new differential integral inequality for non-autonomous Cohen–Grossberg BAM neural networks with finite distributed delays. By using the new inequality and employing some other inequality techniques, we analyze two different types of activation functions which include both bounded and unbounded activation functions. Some easily verifiable criteria are obtained for global exponential attractive sets in which all trajectories converge. These results can also be applied to analyze monostable as well as multistable and more extensive neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. Finally, some examples with numerical simulations are given and analyzed to verify our results.

Suggested Citation

  • Jian, Jigui & Wang, Baoxian, 2015. "Global Lagrange stability for neutral-type Cohen–Grossberg BAM neural networks with mixed time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 116(C), pages 1-25.
    • Handle: RePEc:eee:matcom:v:116:y:2015:i:c:p:1-25
    DOI: 10.1016/j.matcom.2015.04.005
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    References listed on IDEAS

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    1. Xia, Yonghui & Huang, Zhenkun & Han, Maoan, 2008. "Exponential p-stability of delayed Cohen–Grossberg-type BAM neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 806-818.
    2. Wang, Jiafu & Huang, Lihong, 2012. "Almost periodicity for a class of delayed Cohen–Grossberg neural networks with discontinuous activations," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1157-1170.
    3. Li, Kelin & Zeng, Huanglin, 2010. "Stability in impulsive Cohen–Grossberg-type BAM neural networks with time-varying delays: A general analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2329-2349.
    4. Li, Liangliang & Jian, Jigui, 2015. "Exponential p-convergence analysis for stochastic BAM neural networks with time-varying and infinite distributed delays," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 860-873.
    5. 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.
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    Cited by:

    1. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    2. Zheng, Mingwen & Wang, Zeming & Li, Lixiang & Peng, Haipeng & Xiao, Jinghua & Yang, Yixian & Zhang, Yanping & Feng, Cuicui, 2018. "Finite-time generalized projective lag synchronization criteria for neutral-type neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 195-203.
    3. 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.
    4. Kashkynbayev, Ardak & Cao, Jinde & Suragan, Durvudkhan, 2021. "Global Lagrange stability analysis of retarded SICNNs," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

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