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

UDHAYAKUMAR K.; RAKKIYAPPAN R.; CAO Jin-de; TAN Xue-gang

doi:10.1631/FITEE.1900409

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

Special Issue on Complex Systems and Networks with Their Applications | Updated：2022-05-19

- Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks
- 分数阶脉冲四元数神经网络多平衡点的Mittag-Leffler稳定性分析
- Frontiers of Information Technology & Electronic Engineering Vol. 21, Issue 2, Pages: 234-246(2020)
- Affiliations：
  
  Department of Mathematics, Bharathiar University, Coimbatore 641046, India
  School of Mathematics, Southeast University, Nanjing 210096, China
  School of Automation, Southeast University, Nanjing 210096, China
- Author bio：
  
  [ "K. UDHAYAKUMAR, E-mail: udhai512@gmail.com" ]
  [ "R. RAKKIYAPPAN, E-mail: rakkigru@gmail.com" ]
  [ "Jin-de CAO, E-mail: jdcao@seu.edu.cn" ]
  [ "Xue-gang TAN, E-mail: xgtan_sde@163.com" ]
- Funds：
- DOI：10.1631/FITEE.1900409
  CLC： O175
- Received：14 August 2019，
  
  Revised：2019-12-;4，
  
  Published：2020-02
- Accepted：
Scan QR Code
UDHAYAKUMAR K., RAKKIYAPPAN R., CAO Jin-de, et al. 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.
DOI：

UDHAYAKUMAR K., RAKKIYAPPAN R., CAO Jin-de, et al. 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. DOI： 10.1631/FITEE.1900409.

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。

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.

关键词

Keywords

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