Multistability for delayed neural networks via sequential contracting

Chang Yuan Cheng; Kuang Hui Lin; Chih-Wen Shih; Jui Pin Tseng

doi:10.1109/TNNLS.2015.2404801

Multistability for delayed neural networks via sequential contracting

Chang Yuan Cheng, Kuang Hui Lin, Chih-Wen Shih, Jui Pin Tseng

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

In this paper, we explore a variety of new multistability scenarios in the general delayed neural network system. Geometric structure embedded in equations is exploited and incorporated into the analysis to elucidate the underlying dynamics. Criteria derived from different geometric configurations lead to disparate numbers of equilibria. A new approach named sequential contracting is applied to conclude the global convergence to multiple equilibrium points of the system. The formulation accommodates both smooth sigmoidal and piecewiselinear activation functions. Several numerical examples illustrate the present analytic theory.

Original language	English
Article number	7053938
Pages (from-to)	3109-3122
Number of pages	14
Journal	IEEE Transactions on Neural Networks and Learning Systems
Volume	26
Issue number	12
DOIs	https://doi.org/10.1109/TNNLS.2015.2404801
State	Published - 1 Dec 2015

Keywords

Complete stability
Delay equations
Multistability
Neural network

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10.1109/TNNLS.2015.2404801

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abstract = "In this paper, we explore a variety of new multistability scenarios in the general delayed neural network system. Geometric structure embedded in equations is exploited and incorporated into the analysis to elucidate the underlying dynamics. Criteria derived from different geometric configurations lead to disparate numbers of equilibria. A new approach named sequential contracting is applied to conclude the global convergence to multiple equilibrium points of the system. The formulation accommodates both smooth sigmoidal and piecewiselinear activation functions. Several numerical examples illustrate the present analytic theory.",

keywords = "Complete stability, Delay equations, Multistability, Neural network",

author = "Cheng, {Chang Yuan} and Lin, {Kuang Hui} and Chih-Wen Shih and Tseng, {Jui Pin}",

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KW - Complete stability

KW - Delay equations

KW - Multistability

KW - Neural network

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Multistability for delayed neural networks via sequential contracting

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