Lu Jianquan, Ho Daniel W C, Cao Jinde, Kurths Jürgen
Department of Mathematics, Southeast University,Nanjing 210096, China.
IEEE Trans Neural Netw. 2011 Feb;22(2):329-36. doi: 10.1109/TNN.2010.2101081. Epub 2011 Jan 13.
This brief investigates globally exponential synchronization for linearly coupled neural networks (NNs) with time-varying delay and impulsive disturbances. Since the impulsive effects discussed in this brief are regarded as disturbances, the impulses should not happen too frequently. The concept of average impulsive interval is used to formalize this phenomenon. By referring to an impulsive delay differential inequality, we investigate the globally exponential synchronization of linearly coupled NNs with impulsive disturbances. The derived sufficient condition is closely related with the time delay, impulse strengths, average impulsive interval, and coupling structure of the systems. The obtained criterion is given in terms of an algebraic inequality which is easy to be verified, and hence our result is valid for large-scale systems. The results extend and improve upon earlier work. As a numerical example, a small-world network composing of impulsive coupled chaotic delayed NN nodes is given to illustrate our theoretical result.
本文研究具有时变延迟和脉冲干扰的线性耦合神经网络（NNs）的全局指数同步问题。由于本文所讨论的脉冲效应被视为干扰，脉冲不应过于频繁地发生。平均脉冲间隔的概念用于形式化这一现象。通过参考一个脉冲延迟微分不等式，我们研究了具有脉冲干扰的线性耦合神经网络的全局指数同步。导出的充分条件与系统的时间延迟、脉冲强度、平均脉冲间隔和耦合结构密切相关。所得到的准则以一个易于验证的代数不等式给出，因此我们的结果对大规模系统是有效的。这些结果扩展并改进了早期的工作。作为一个数值例子，给出了一个由脉冲耦合混沌延迟神经网络节点组成的小世界网络来说明我们的理论结果。
