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New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality.
Neural Networks ( IF 6.0 ) Pub Date : 2019-11-04 , DOI: 10.1016/j.neunet.2019.10.017
Jianying Xiao 1 , Shiping Wen 2 , Xujun Yang 3 , Shouming Zhong 4
Affiliation  

In this paper, a novel kind of neural networks named fractional-order quaternion-valued bidirectional associative memory neural networks (FQVBAMNNs) is formulated. On one hand, applying Hamilton rules in quaternion multiplication which is essentially non-commutative, the system of FQVBAMNNs is separated into eight fractional-order real-valued systems. Meanwhile, the activation functions are considered to be quaternion-valued linear threshold ones which help to reduce the unnecessary computational complexity. On the other hand, based on fractional-order Lyapunov technology, a new fractional-order derivative inequality is established. Mainly by employing the new inequality technique, constructing three novel Lyapunov-Krasovskii functionals (LKFs) and designing simple linear controllers, the global Mittag-Leffler synchronization problems are investigated and the corresponding criteria are acquired for the system of FQVBAMNNs and its special cases such as fractional-order complex-valued BAM neural networks (FCVBAMNNs) and fractional-order real-valued BAM neural networks (FRVBAMNNs), respectively. Finally, two numerical examples are given to show the effectiveness and availability of the proposed results.

中文翻译:

基于新不等式的分数阶四元数值BAM神经网络全局Mittag-Leffler同步问题的新方法。

本文提出了一种新型的神经网络,称为分数阶四元数值双向联想记忆神经网络(FQVBAMNNs)。一方面,在四元数乘法中应用汉密尔顿规则,该四元数乘法本质上是不可交换的,FQVBAMNNs系统被分为八个分数阶实数值系统。同时,激活函数被认为是四元数值线性阈值函数,有助于降低不必要的计算复杂性。另一方面,基于分数阶Lyapunov技术,建立了一个新的分数阶导数不等式。主要通过采用新的不等式技术,构造三个新颖的Lyapunov-Krasovskii函数(LKF)并设计简单的线性控制器,研究了全球Mittag-Leffler同步问题,并为FQVBAMNNs系统及其特殊情况(例如分数阶复值BAM神经网络(FCVBAMNNs)和分数阶实值BAM神经网络(FRVBAMNNs))确定了相应的标准), 分别。最后,给出了两个数值例子来说明所提出的结果的有效性和有效性。
更新日期:2019-11-04
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