An Overview of the Stability Analysis of Recurrent Neural Networks With Multiple Equilibria

被引：41

作者：

Liu, Peng ^{[1
,2
]}

Wang, Jun ^{[3
]}

Zeng, Zhigang ^{[4
,5
]}

机构：

[1] Zhengzhou Univ Light Ind, Sch Elect & Informat Engn, Zhengzhou 450002, Peoples R China

[2] Henan Key Lab Informat Based Elect Appliances, Zhengzhou 450002, Peoples R China

[3] City Univ Hong Kong, Sch Data Sci, Dept Comp Sci, Hong Kong, Peoples R China

[4] Huazhong Univ Sci & Technol, Sch Artificial Intelligence & Automat, Wuhan 430074, Peoples R China

[5] Educ Minist China, Key Lab Image Proc & Intelligent Control, Wuhan 430074, Peoples R China

来源：

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS | 2023年 / 34卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Stability criteria; Switches; Recurrent neural networks; Mathematical model; Stairs; Delay effects; Analytical models; Complete stability; multiple equilibria; multistability; recurrent neural networks (RNNs); LINEAR ACTIVATION FUNCTIONS; LIMIT SET DICHOTOMY; MU-STABILITY; MULTISTABILITY ANALYSIS; ASSOCIATIVE MEMORY; LOCAL STABILITY; GENERAL-CLASS; CONVERGENCE; MULTIPERIODICITY; DYNAMICS;

D O I：

10.1109/TNNLS.2021.3105519

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The stability analysis of recurrent neural networks (RNNs) with multiple equilibria has received extensive interest since it is a prerequisite for successful applications of RNNs. With the increasing theoretical results on this topic, it is desirable to review the results for a systematical understanding of the state of the art. This article provides an overview of the stability results of RNNs with multiple equilibria including complete stability and multistability. First, preliminaries on the complete stability and multistability analysis of RNNs are introduced. Second, the complete stability results of RNNs are summarized. Third, the multistability results of various RNNs are reviewed in detail. Finally, future directions in these interesting topics are suggested.

引用

页码：1098 / 1111

页数：14

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