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

Yang, Xujun; Li, Chuandong; Song, Qiankun; Chen, Jian-Zhang; Huang, Junjian

doi:10.1016/j.neunet.2018.04.015

Cited by 117 publications

(43 citation statements)

References 44 publications

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“…Remark Hong‐Li et al dealt with the asymptotic synchronization of fractional order complex dynamical networks by using pinning adaptive impulsive control. Xujun et al investigated the global Mittag‐Leffler stability and synchronization of FNNs with linear threshold neurons in quaternion field by designing simple linear feedback control. However, the adaptive impulsive synchronization of FNNs in quaternion field has not been considered in the existing works.…”

Section: Synchronization Via Adaptive Impulsive Controlmentioning

confidence: 99%

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Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

Anbalagan

Raja

Alzabut

et al. 2020

Math Methods in App Sciences

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Fractional order quaternion‐valued neural networks are a type of fractional order neural networks for which neuron state, synaptic connection strengths, and neuron activation functions are quaternion. This paper is dealing with the Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field. The fractional order quaternion‐valued neural networks are separated into four real‐valued systems forming an equivalent four real‐valued fractional order neural networks, which decreases the computational complexity by avoiding the noncommutativity of quaternion multiplication. Via some fractional inequality techniques and suitable Lyapunov functional, a brand new criterion is proposed first to ensure the Mittag‐Leffler stability for the addressed neural networks. Besides, the combination of quaternion‐valued adaptive and impulsive control is intended to realize the asymptotically synchronization between two fractional order quaternion‐valued neural networks. Ultimately, two numerical simulations are provided to check the accuracy and validity of our obtained theoretical results.

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Section: Synchronization Via Adaptive Impulsive Controlmentioning

confidence: 99%

“…But there is little attention about the dynamics of FQNNs have been found in the existing literatures. For example, Yang et al presented the Mittag‐Leffler stability and Mittag‐Leffler synchronization analysis of FQNNs with linear threshold neurons.…”

Section: Introductionmentioning

confidence: 99%

Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

Anbalagan

Raja

Alzabut

et al. 2020

Math Methods in App Sciences

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show abstract

“…Then, according to Lemmas 3, 7 and (29), we do the following calculations: Remark 4 In Theorems 1, 2 and 3, the LMI conditions for the global Mittag-Leffler stability, robust stability and projection synchronization of FQVNNs by Lyapunov stability theory were given, respectively. Unlike the methods in the existing literature [35,41,44], we considered FQVNNs directly instead of converting them into complex-valued or realvalued system.…”

Section: Construct a Lyapunov Function As Followsmentioning

confidence: 99%

“…In [44], the global Mittag-Leffler stability problem for FQVNNs is considered. If we use Theorem 3 in [44] to test the existence and Mittag-Leffler stability of the equilibrium point of FQVNNs (37) in Example 1 of our article. We need checkĈ -|Â|, defined in [44], is a non-singular M-matrix.…”

Section: Remarkmentioning

confidence: 99%

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LMI conditions for some dynamical behaviors of fractional-order quaternion-valued neural networks

Lin

Chen

et al. 2019

Adv Differ Equ

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This paper addresses the issue of three dynamical behaviors including global Mittag-Leffler stability, robust stability and projection synchronization for fractional-order quaternion-valued neural networks (FQVNNs). Some linear matrix inequality conditions for these dynamical behaviors of FQVNNs are given by Lyapunov stability theory, quaternion matrix theory, Homeomorphic mapping theory and fractional differential equation theory. Furthermore, these obtained sufficient conditions for stability and synchronization are superior to those in existing literature. Finally, three examples are given to illustrate the effectiveness of the theoretical results.

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Global projective synchronization in fractional‐order quaternion valued neural networks

Zhang

Cao

et al. 2020

Asian Journal of Control

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The analysis of projective synchronization for fractional-order quaternion valued neural networks (FOQVNN) is addressed in this paper. The FOQVNN is separated into four real valued parts through Hamilton rules, enabling its synchronization analysis. Some criteria are formulated by the use of fractional differential inequality techniques; projective synchronization of FOQVNN is implemented by designing suitable hybrid controllers. One numerical example is given to show the feasibility of proposed methods.

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

Cited by 117 publications

References 44 publications

Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

LMI conditions for some dynamical behaviors of fractional-order quaternion-valued neural networks

Global projective synchronization in fractional‐order quaternion valued neural networks

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