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Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (4): 428-440    DOI:
    
Global exponential stability and Hopf bifurcation of inertial Cohen-Grossberg neural networks with time delays in leakage terms
TIAN Xiao-hong, XU Rui, WANG Zhi-li
Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China
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Abstract  In this paper, a class of inertial Cohen-Grossberg neural networks with time delays in leakage terms is investigated. By constructing the appropriate Lyapunov functional, sufficient conditions are obtained for the global exponential stability of the equilibrium. By analyzing the corresponding characteristic equation, the local stability of the equilibrium and the existence of Hopf bifurcation are established. Numerical simulations are carried out to illustrate the main results.

Key wordsinertial Cohen-Grossberg neural networks      leakage delays      Hopf bifurcation      global exponential stability     
Received: 26 January 2016      Published: 16 May 2018
CLC:  O175.1  
Cite this article:

TIAN Xiao-hong, XU Rui, WANG Zhi-li. Global exponential stability and Hopf bifurcation of inertial Cohen-Grossberg neural networks with time delays in leakage terms. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4): 428-440.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2016/V31/I4/428


一类具有Leakage时滞的惯性Cohen-Grossberg神经网络的全局指数稳定性和Hopf分支

研究一类具有Leakage时滞的惯性Cohen-Grossberg神经网络模型. 通过构造适当的Lyapunov泛函得到了平衡点全局指数稳定的充分条件. 通过分析特征方程, 讨论了系统平衡点的局部稳定性, 得出了系统Hopf分支存在的充分条件. 最后对所得理论结果进行了数值模拟.

关键词: 惯性Cohen-Grossberg神经网络模型,  Leakage时滞,  Hopf分支,  全局指数稳定性 
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