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

摘要

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.%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.