具反应扩散混合时滞Cohen-Grossberg神经网络的指数耗散性

利用扩散算子特性、M-矩阵性质和不等式分析技巧,在不要求神经网络激励函数的有界性、单调性、可微性以及平均时滞有界性的弱保守条件下,研究了一类具有反应扩散混合时滞的非自治Cohen-Grossberg神经网络的实不变集、全局指数稳定性和指数耗散性,并给出了相关的充分性条件.文中所使用的方法摒弃了常规构造适当的Lyapunov泛函的方法,克服了Lyapunov泛函难构造的困难,且得到的结果扩展和改进了其他文献结果.最后给出了一个数值例子来说明所得结果的有效性.

Exponential dissipativity of Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms

Without assuming the boundedness,monotonicity and differentiability of the activation functions and the boundedness of average time delays,the invariant set,global exponential stability and exponential dissipativity of a class of Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms are studied by employing the properties of diffusion operator,M-matrix and inequality technique.Some correlative sufficient conditions are then derived.The method used in this paper ignores the common requirement of constructing proper Lyapunov functionals,thus eliminat- ing the difficulty in building proper Lyapunov functionals.Moreover,the results extend and improve the prior results in publications.Finally,a numerical example is given to illustrate the effectiveness of the results.