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CLC number: O175

On-line Access: 2020-03-04

Received: 2019-08-14

Revision Accepted: 2019-10-19

Crosschecked: 2019-12-04

Cited: 0

Clicked: 825

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

K. Udhayakumar

https://orcid.org/0000-0001-5764-1990

Jin-de Cao

https://orcid.org/0000-0003-3133-7119

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Frontiers of Information Technology & Electronic Engineering  2020 Vol.21 No.2 P.234-246

http://doi.org/10.1631/FITEE.1900409


Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks


Author(s):  K. Udhayakumar, R. Rakkiyappan, Jin-de Cao, Xue-gang Tan

Affiliation(s):  Department of Mathematics, Bharathiar University, Coimbatore 641046, India; more

Corresponding email(s):   udhai512@gmail.com, rakkigru@gmail.com, jdcao@seu.edu.cn, xgtan_sde@163.com

Key Words:  Mittag-Leffler stability, Fractional-order, Quaternion-valued neural networks, Impulse


K. Udhayakumar, R. Rakkiyappan, Jin-de Cao, Xue-gang Tan. Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 234-246.

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author="K. Udhayakumar, R. Rakkiyappan, Jin-de Cao, Xue-gang Tan",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="21",
number="2",
pages="234-246",
year="2020",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1900409"
}

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%T Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks
%A K. Udhayakumar
%A R. Rakkiyappan
%A Jin-de Cao
%A Xue-gang Tan
%J Frontiers of Information Technology & Electronic Engineering
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%P 234-246
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%D 2020
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1900409

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T1 - Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks
A1 - K. Udhayakumar
A1 - R. Rakkiyappan
A1 - Jin-de Cao
A1 - Xue-gang Tan
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 21
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SP - 234
EP - 246
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Y1 - 2020
PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1900409


Abstract: 
In this study, we investigate the problem of multiple mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks (QVNNs) with impulses. Using the geometrical properties of activation functions and the Lipschitz condition, the existence of the equilibrium points is analyzed. In addition, the global mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order QVNNs is investigated by employing the Lyapunov direct method. Finally, simulation is performed to illustrate the effectiveness and validity of the main results obtained.

分数阶脉冲四元数神经网络多平衡点的Mittag-Leffler稳定性分析

K. UDHAYAKUMAR1,R. RAKKIYAPPAN1,曹进德2,谭学刚3
1巴拉蒂亚大学数学系,印度哥印拜陀市,641046
2东南大学数学学院,中国南京市,210096
3东南大学自动化学院,中国南京市,210096

摘要:研究分数阶四元数值神经网络(quaternion-valued neural networks, QVNNs)的多重Mittag-Leffler稳定性问题。利用激活函数的几何性质和李普希茨条件,分析系统平衡点的存在性。此外,利用李雅普诺夫直接法研究分数阶脉冲四元素神经网络的多平衡点的全局Mittag-Leffler稳定性。最后,通过仿真验证主要结果的有效性和可行性。

关键词:Mittag-Leffler稳定性;分数阶;四元数神经网络;脉冲

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

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