Complete stability of delayed recurrent neural networks with Gaussian activation functions.
This paper addresses the complete stability of delayed recurrent neural networks with Gaussian activation functions. By means of the geometrical properties of Gaussian function and algebraic properties of nonsingular M-matrix, some sufficient conditions are obtained to ensure that for an n-neuron neural network, there are exactly 3kequilibrium points with 0≤k≤n, among which 2kand 3k-2kequilibrium points are locally exponentially stable and unstable, respectively. Moreover, it concludes that all the states converge to one of the equilibrium points; i.e., the neural networks are completely stable. The derived conditions herein can be easily tested. Finally, a numerical example is given to illustrate the theoretical results.
School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China. Electronic address: liupengjz@163.com.
Peng
P
Liu
School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China. Electronic address: zgzeng@hust.edu.cn.
Zhigang
Z
Zeng
Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong. Electronic address: jwang.cs@cityu.edu.hk.
Jun
J
Wang
D000465:Algorithms; D016571:Neural Networks, Computer; D016011:Normal Distribution; D013997:Time Factors
Complete stability; Gaussian functions; Recurrent neural networks; Time-varying delays