School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu, 610106, China.
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610050, China.
Neural Netw. 2022 Oct;154:491-507. doi: 10.1016/j.neunet.2022.07.031. Epub 2022 Aug 2.
In this paper, a new case of neural networks called fractional-order octonion-valued bidirectional associative memory neural networks (FOOVBAMNNs) is established. First, the higher dimensional models are formulated for FOOVBAMNNs with general activation functions and the special linear threshold ones, respectively. On one hand, employing Cayley-Dichson construction in octonion multiplication which is essentially neither commutative nor associative, the system of FOOVBAMNNs is divided into four fractional-order complex-valued ones. On the other hand, Caputo fractional derivative's character and BAM's interactive feature are also properly dealt with. Second, the general criteria are obtained by the new design of LKFs, the application of the related inequalities and the construction of the linear feedback controllers for the global Mittag-Leffler synchronization problem of FOOVBAMNNs. Finally, we present two numerical examples to show the realizability and progress of the derived results.
本文建立了一种新的神经网络，称为分数阶八元数值双向联想记忆神经网络（FOOVBAMNNs）。首先，针对具有一般激活函数和特殊线性阈值的 FOOVBAMNNs，分别建立了高维模型。一方面，在八元数乘法中利用 Cayley-Dichson 构造，该乘法本质上既不交换也不结合，将 FOOVBAMNNs 系统分为四个分数阶复值系统。另一方面，适当处理 Caputo 分数阶导数的性质和 BAM 的交互特性。其次，通过 LKFs 的新设计、相关不等式的应用和线性反馈控制器的构建，得到了 FOOVBAMNNs 全局 Mittag-Leffler 同步问题的一般准则。最后，通过两个数值例子验证了所得到的结果的有效性和优越性。
