Multistability of complex-valued neural networks with discontinuous activation functions

被引：82
作者：
Liang, Jinling [1 ]
Gong, Weiqiang [1 ]
Huang, Tingwen [2 ]
机构：
[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China
[2] Texas A&M Univ, Sci Program, Doha, Qatar
来源：
NEURAL NETWORKS | 2016年 / 84卷
基金：
中国国家自然科学基金;
关键词：
Complex-valued neural networks; Multistability; Discontinuous function; Attraction basin; TIME-VARYING DELAYS; MULTIPLE MU-STABILITY; ASSOCIATIVE MEMORY; GLOBAL STABILITY; LOCAL STABILITY; ALGORITHM; RELAXATION; EQUILIBRIA; DYNAMICS; MODEL;
D O I：
10.1016/j.neunet.2016.08.008
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, based on the geometrical properties of the discontinuous activation functions and the Brouwer's fixed point theory, the multistability issue is tackled for the complex-valued neural networks with discontinuous activation functions and time-varying delays. To address the network with discontinuous functions, Filippov solution of the system is defined. Through rigorous analysis, several sufficient criteria are obtained to assure the existence of 25(n) equilibrium points. Among them, 9(n) points are locally stable and 16(n) - 9(n) equilibrium points are unstable. Furthermore, to enlarge the attraction basins of the 9(n) equilibrium points, some mild conditions are imposed. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码：125 / 142
页数：18
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