School of Mathematics, Hefei University of Technology, Hefei, 230009, China.
School of Mathematics, Southeast University, Nanjing 210096, China.
Neural Netw. 2019 Sep;117:285-294. doi: 10.1016/j.neunet.2019.05.024. Epub 2019 Jun 6.
In this paper, the exponential synchronization of the impulsive coupled delayed complex-valued neural networks (CVNNs) is studied. Without constructing the Lyapunov function, a novel approach based on the matrix measure and extended Halanay inequality is presented and some sufficient criteria for exponential synchronization of the addressed CVNNs are derived. In this paper, the restriction of the real and imaginary parts of activation functions which are supposed to depend only on the real and imaginary parts of the variables, respectively, is removed. Furthermore, by employing the average impulsive interval method, the requirement on the upper bound of the impulsive intervals is removed for impulsive signal transmission. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results obtained, even for large-scale CVNNs with impulsive coupling.
本文研究了脉冲耦合时滞复值神经网络（CVNNs）的指数同步问题。在不构造 Lyapunov 函数的情况下，提出了一种基于矩阵测度和推广的 Halanay 不等式的新方法，并导出了所研究的 CVNNs 指数同步的一些充分条件。在本文中，取消了激活函数的实部和虚部的限制，激活函数仅分别依赖于变量的实部和虚部。此外，通过采用平均脉冲间隔方法，去除了脉冲信号传输对脉冲间隔上界的要求。最后，通过数值例子验证了所得理论结果的有效性，即使对于具有脉冲耦合的大规模 CVNNs 也是如此。
