Coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions

doi:10.1088/1674-1056/28/4/040701

中国物理B ›› 2019, Vol. 28 ›› Issue (4): 40701-040701.doi: 10.1088/1674-1056/28/4/040701

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions

Yu-Jiao Huang(黄玉娇), Shi-Jun Chen(陈时俊), Xu-Hua Yang(杨旭华), Jie Xiao(肖杰)

College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China

收稿日期:2018-09-06 修回日期:2018-12-03 出版日期:2019-04-05 发布日期:2019-04-05
通讯作者: Yu-Jiao Huang E-mail:hyj0507@zjut.edu.cn
基金资助:
Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LY18F030023, LY17F030016, and LY18F020028) and the National Natural Science Foundation of China (Grant Nos. 61503338, 61502422, and 61773348).

Coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions

Yu-Jiao Huang(黄玉娇), Shi-Jun Chen(陈时俊), Xu-Hua Yang(杨旭华), Jie Xiao(肖杰)

College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China

Received:2018-09-06 Revised:2018-12-03 Online:2019-04-05 Published:2019-04-05
Contact: Yu-Jiao Huang E-mail:hyj0507@zjut.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LY18F030023, LY17F030016, and LY18F020028) and the National Natural Science Foundation of China (Grant Nos. 61503338, 61502422, and 61773348).

摘要/Abstract

摘要：

In this paper, coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag-Leffler stability, sufficient criteria are established to ensure the existence of (2k+3)ⁿ (k ≥ 1) equilibrium points, among which (k+2)ⁿ equilibrium points are locally Mittag-Leffler stable. Compared with the existing results, the derived results cover local Mittag-Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.

关键词: fractional-order recurrent neural network, local Mittag-Leffler stability, discontinuous activation function

Abstract:

Key words: fractional-order recurrent neural network, local Mittag-Leffler stability, discontinuous activation function

中图分类号: (Neural networks, fuzzy logic, artificial intelligence)

07.05.Mh

02.30.Ks (Delay and functional equations)

黄玉娇, 陈时俊, 杨旭华, 肖杰. Coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions[J]. 中国物理B, 2019, 28(4): 40701-040701.

Yu-Jiao Huang(黄玉娇), Shi-Jun Chen(陈时俊), Xu-Hua Yang(杨旭华), Jie Xiao(肖杰). Coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions[J]. Chin. Phys. B, 2019, 28(4): 40701-040701.

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Coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions

Coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions

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