基于时间尺度理论研究非自治模糊细胞神经网络的全局指数稳定性  

Global Exponential Stability of Non-autonomous FCNNs with Dirichlet Boundary Conditions and Reaction-diffusion Terms on Time Scales

作　　者：吕小俊[1] 张天伟[2] 赵凯宏[3] LV Xiaojun ZHANG Tianwei ZHAO Kaihong(Department of Information Science and Technology, Tourism and Culture College of Yunnan University, Lijiang 674199, China Section of General Core Courses in City College, Kunming University of Science and Technology, Kunming 650051, China Department of Applicate Maths, Kunming University of Science and Technology, Kunming 650093, China)

机构地区：[1]云南大学旅游文化学院信息科学与技术系,丽江674199 [2]昆明理工大学城市学院,昆明650051 [3]昆明理工大学应用数学系,昆明650093

出　　处：《应用泛函分析学报》2016年第3期314-325,共12页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11161025);云南大学旅游文化学院重点项目(2015XYZ03)

摘　　要：通过使用叠合度理论、M-矩阵、李雅谱诺夫函数和不等式技巧等,在时间尺度上研究带有狄利克雷边值和反应扩散项的非自治模糊细胞神经网络的全局指数稳定性,并获得一些使其存在全局指数稳定的平衡点的充分条件.最后,给出一个例子去验证结论的有效性.In this paper, the global exponential stability of equilibrium solution to non-autonomous fuzzy cellular neural networks with Dirichlet boundary conditions and reaction-diffusion terms on time scales is studied. Using topological degree theory, M-matrix method, Lyapunov functional and inequality skills, we find some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for non-autonomous fuzzy cellular neural networks with Dirichlet boundary conditions and reaction-diffusion terms on time scales. An example is given to show the effectiveness of the obtained results.

关 键 词：全局指数稳定 模糊细胞神经网络 狄利克雷边值 时间尺度 反应扩散 

分 类 号：O175.14[理学—数学]