基于无穷时滞细胞神经网络的稳定性分析:连续和离散模型（英文）  

Stability of Cellular Neural Networks with Infinite Delays: Continuous-time and Discrete-time Cases

作　　者：夏合旦.哈力丁 蒋海军[1] 王金铃 Xiahedan Haliding;JIANG Haijun;WANG Jinling(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）》2018年第3期289-294,313,共7页Journal of Xinjiang University(Natural Science Edition)

基　　金：supported by National Natural Science Foundation of People’s Republic of China(61473244)

摘　　要：首先,利用泛函微分方程、稳定性分析、Lyapunov泛函等理论,我们研究了具有无穷时滞连续细胞神经网络的动力学行为,并得到了其平衡点的存在性、唯一性以及全局指数稳定的充分条件;其次,我们利用半离散化方法,得到了连续系统的离散化模型,并对其动力学行为进行了分析;最后,我们通过数值模拟验证了本文的结论是真实有效的.In this paper, the stability of cellular neural networks（CNNs） is investigated. Firstly, based on the theories of functional differential equations, stability analysis and Lyapunov functional, we study the dynamical behaviors of continuous-time cellular neural networks with infinite delays and some sufficient conditions are achieved to guarantee its equilibrium point which uniquely exist, and is globally exponentially stable. Secondly, we obtain the discrete-time analogues of the continuous-time systems via the semi-discretization technique and also investigate its dynamic behaviors.Finally, the numerical simulation is used to validate the validity of proposed approaches.

关 键 词：连续细胞神经网络 离散细胞神经网络 无穷时滞 LYAPUNOV泛函 全局指数稳定性 全局渐进稳定性 

分 类 号：O175.7[理学—数学]