School of Sciences, Southwest Petroleum University, Chengdu, 610050, PR China.
School of Computer Science and Engineering, University of Electronic Science and Technology, Chengdu, 611731, PR China.
Neural Netw. 2020 Feb;122:320-337. doi: 10.1016/j.neunet.2019.10.017. Epub 2019 Nov 4.
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.
本文提出了一种新的神经网络，称为分数阶四元数值双向联想记忆神经网络（FQVBAMNNs）。一方面，在本质上非交换的四元数乘法中应用哈密尔顿法则，将 FQVBAMNNs 系统分解为八个分数阶实值系统。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度。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。主要通过利用新的不等式技术，构造三个新的 Lyapunov-Krasovskii 泛函（LKFs）并设计简单的线性控制器，研究了 FQVBAMNNs 及其特殊情况（如分数阶复值双向联想记忆神经网络（FCVBAMNNs）和分数阶实值双向联想记忆神经网络（FRVBAMNNs））的全局 Mittag-Leffler 同步问题，并获得了相应的准则。最后，给出了两个数值示例，以验证所提出结果的有效性和实用性。
