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

Peng Liu; Jun Wang; Zhigang Zeng

doi:10.1109/TNNLS.2021.3105519

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

Peng Liu, Jun Wang^*, Zhigang Zeng

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

47 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1098-1111
Number of pages	14
Journal	IEEE Transactions on Neural Networks and Learning Systems
Volume	34
Issue number	3
Online published	27 Aug 2021
DOIs	https://doi.org/10.1109/TNNLS.2021.3105519
Publication status	Published - Mar 2023

Research Keywords

Analytical models
Complete stability
Delay effects
Mathematical model
multiple equilibria
multistability
Recurrent neural networks
recurrent neural networks (RNNs)
Stability criteria
Stairs
Switches

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title = "An Overview of the Stability Analysis of Recurrent Neural Networks With Multiple Equilibria",

abstract = "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.",

keywords = "Analytical models, Complete stability, Delay effects, Mathematical model, multiple equilibria, multistability, Recurrent neural networks, recurrent neural networks (RNNs), Stability criteria, Stairs, Switches",

author = "Peng Liu and Jun Wang and Zhigang Zeng",

year = "2023",

month = mar,

doi = "10.1109/TNNLS.2021.3105519",

language = "English",

volume = "34",

pages = "1098--1111",

journal = "IEEE Transactions on Neural Networks and Learning Systems",

issn = "2162-237X",

publisher = "IEEE Computational Intelligence Society",

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T1 - An Overview of the Stability Analysis of Recurrent Neural Networks With Multiple Equilibria

AU - Liu, Peng

AU - Wang, Jun

AU - Zeng, Zhigang

PY - 2023/3

Y1 - 2023/3

N2 - 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.

AB - 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.

KW - Analytical models

KW - Complete stability

KW - Delay effects

KW - Mathematical model

KW - multiple equilibria

KW - multistability

KW - Recurrent neural networks

KW - recurrent neural networks (RNNs)

KW - Stability criteria

KW - Stairs

KW - Switches

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U2 - 10.1109/TNNLS.2021.3105519

DO - 10.1109/TNNLS.2021.3105519

M3 - RGC 21 - Publication in refereed journal

SN - 2162-237X

VL - 34

SP - 1098

EP - 1111

JO - IEEE Transactions on Neural Networks and Learning Systems

JF - IEEE Transactions on Neural Networks and Learning Systems

IS - 3

ER -

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

Abstract

Research Keywords

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GRF: Collaborative Neurodynamic Approaches to Portfolio Optimization

GRF: Intelligent Mission Planning and Tracking Control of Autonomous Surface Vehicles Based on Neural Computation

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

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Research Keywords

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GRF: Collaborative Neurodynamic Approaches to Portfolio Optimization

GRF: Intelligent Mission Planning and Tracking Control of Autonomous Surface Vehicles Based on Neural Computation

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