Jiang Haijun, Teng Zhidong
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China.
Neural Netw. 2006 Jun;19(5):676-83. doi: 10.1016/j.neunet.2005.06.050. Epub 2005 Sep 29.
This paper studies the general neural networks dynamical systems with variable coefficients and time-varying delays. By applying the Young inequality technique, Dini derivative and introducing many real parameters, and estimating the upper bound of solutions of the system, a series of new and useful criteria on the boundedness, global exponential stability and the existence and global exponential stability of the periodic solutions are established. Particularly, when the system degenerates into the autonomous case, the new criteria on the existence, uniqueness and global exponential stability of the equilibrium points are obtained. The results obtained in this paper extend and generalize the corresponding results existing in previous literature.
本文研究了具有变系数和时变时滞的一般神经网络动力系统。通过应用杨氏不等式技巧、迪尼导数并引入多个实参数，以及估计系统解的上界，建立了一系列关于有界性、全局指数稳定性以及周期解的存在性和全局指数稳定性的新的有用准则。特别地，当系统退化为自治情形时，得到了关于平衡点的存在性、唯一性和全局指数稳定性的新准则。本文所得结果扩展并推广了先前文献中存在的相应结果。
