Extended analysis on the global Mittag-Leffler synchronization problem for fractional-order octonion-valued BAM neural networks
Extended analysis on the global Mittag-Leffler synchronization problem for fractional-order octonion-valued BAM neural networks
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DOI：
10.1016/j.neunet.2022.07.031
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发表时间：
2022-08
期刊：
影响因子：
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通讯作者：
Jianying Xiao;Xiao-bo Guo;Yongtao Li;S. Wen;Kaibo Shi;Yiqian Tang
中科院分区：
文献类型：
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作者：
Jianying Xiao;Xiao-bo Guo;Yongtao Li;S. Wen;Kaibo Shi;Yiqian Tang
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，分别建立了具有一般激活函数和特殊线性阈值函数的FOOVBAMNN的高维模型。一方面，利用Cayley-Dichson构造法将FOOVBAMNN系统分解为四个分数阶复值系统，该构造法本质上既不是可交换的，也不是结合的。另一方面，对Caputo分数阶导数的性质和BAM的交互作用特性也作了适当的处理。其次，通过新的LKF设计、相关不等式的应用以及FOOVBAMNN全局Mittag-Leffler同步问题的线性反馈控制器的构造，获得了FOOVBAMNN全局Mittag-Leffler同步问题的一般准则。最后，我们给出了两个数值例子，以显示所得到的结果的可实现性和进展。
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.