多比例时滞细胞神经网络的指数周期性与稳定性  

Exponential Periodicity and Stability of Cellular Neural Networks with Multi-Pantograph Delays

作　　者：周立群[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《生物数学学报》2012年第3期480-488,共9页Journal of Biomathematics

基　　金：国家自然科学基金资助项目(60974144);天津市高等学校科技发展基金项目(20100813);天津师范大学博士基金项目(52LX34)

摘　　要：研究了一类具多比例时滞细胞神经网络的全局指数周期性与稳定性.通过变换y(t)=x(e^t)将具多比例时滞的细胞神经网络变换成具常时滞变系数的细胞神经网络,利用一些分析技巧与构造合适的Lyapunov泛函,得到系统的周期解存在唯一且全局指数周期的时滞依赖的充分条件,判断方法简单易验证.并给出了两个例子及其数值仿真结果以支持所得结论.The global exponential periodicity and the global exponential stability are investigated for cellular neural networks with multi-pantograph delays.The transformationy（t） = x（e^t）transforms the cellular neural networks with multi-pantograph delays into the cellular neural networks with constant delays and variable coefficients.By applying some analysis techniques and constructing a suitable Lyapunov functional,some new delay-dependent sufficient conditions are derived for ensuring the existence and uniqueness of periodic solution and global exponential periodicity and stability,which are easily verifiable.And two examples and their numerical simulations are given to support the obtained conclusion.

关 键 词：细胞神经网络 比例时滞 全局指数周期性 全局指数稳定性 LYAPUNOV泛函 

分 类 号：O175.12[理学—数学] TP183[理学—基础数学]