Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons

Xujun Yang; Chuandong Li; Qiankun Song; Jiyang Chen; Junjian Huang

doi:10.1016/j.neunet.2018.04.015

Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons

Neural Netw. 2018 Sep:105:88-103. doi: 10.1016/j.neunet.2018.04.015. Epub 2018 May 4.

Authors

Xujun Yang¹, Chuandong Li², Qiankun Song³, Jiyang Chen⁴, Junjian Huang⁵

Affiliations

¹ Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, PR China. Electronic address: xujunyangcquc@163.com.
² Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, PR China. Electronic address: cdli@swu.edu.cn.
³ College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, PR China. Electronic address: qiankunsong@163.com.
⁴ Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, PR China. Electronic address: 18716622493@163.com.
⁵ Department of Computer Science, Chongqing University of Education, Chongqing 400067, PR China. Electronic address: hmomu@sina.com.

PMID: 29793129
DOI: 10.1016/j.neunet.2018.04.015

Abstract

This paper talks about the stability and synchronization problems of fractional-order quaternion-valued neural networks (FQVNNs) with linear threshold neurons. On account of the non-commutativity of quaternion multiplication resulting from Hamilton rules, the FQVNN models are separated into four real-valued neural network (RVNN) models. Consequently, the dynamic analysis of FQVNNs can be realized by investigating the real-valued ones. Based on the method of M-matrix, the existence and uniqueness of the equilibrium point of the FQVNNs are obtained without detailed proof. Afterwards, several sufficient criteria ensuring the global Mittag-Leffler stability for the unique equilibrium point of the FQVNNs are derived by applying the Lyapunov direct method, the theory of fractional differential equation, the theory of matrix eigenvalue, and some inequality techniques. In the meanwhile, global Mittag-Leffler synchronization for the drive-response models of the addressed FQVNNs are investigated explicitly. Finally, simulation examples are designed to verify the feasibility and availability of the theoretical results.

Keywords: Fractional order; Mittag-Leffler synchronization; Mittag-leffler stability; Quaternion-valued neural networks.

MeSH terms

Neural Networks, Computer*