Multistability analysis of quaternion-valued neural networks with cosine activation functions *

被引：9

作者：

Yu, Siyi ^{[1
]}

Li, Hua ^{[1
]}

Chen, Xiaofeng ^{[1
]}

Lin, Dongyuan ^{[2
]}

机构：

[1] Chongqing Jiaotong Univ, Dept Math, Chongqing 400074, Peoples R China

[2] Southwest Univ, Coll Elect & Informat Engn, Chongqing 400715, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2023年 / 445卷

基金：

中国国家自然科学基金;

关键词：

Multistability; Quaternion-valued neural networks; Attraction basins; Cosine activation function; ASSOCIATIVE MEMORY; COMPLETE STABILITY;

D O I：

10.1016/j.amc.2023.127849

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is significant to design a system with high storage capacity for associative memory and pattern recognition. To address this issue, this paper first proposes a quaternion-valued neural network (QVNN) model with multiple equilibrium points in which the cosine function is used as the activation function of QVNN. Then, based on the Brouwer fixed point theorem and the geometric properties of the activation function, sufficient conditions for QVNN to have unique equilibrium points, finite equilibrium points, and countable infinite equilibrium points are obtained, respectively. Furthermore, sufficient conditions for the exponential stability of equilibrium points are derived, and the attraction basins of the stable equilibrium points are given. Finally, two numerical examples are given to confirm the validity of the proposed theoretical results.

引用

页数：16

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