Extended analysis on the global Mittag-Leffler synchronization problem for fractional-order octonion-valued BAM neural networks

Jianying Xiao; Xiao Guo; Yongtao Li; Shiping Wen; Kaibo Shi; Yiqian Tang

doi:10.1016/j.neunet.2022.07.031

Extended analysis on the global Mittag-Leffler synchronization problem for fractional-order octonion-valued BAM neural networks

Neural Netw. 2022 Oct:154:491-507. doi: 10.1016/j.neunet.2022.07.031. Epub 2022 Aug 2.

Authors

Jianying Xiao¹, Xiao Guo², Yongtao Li³, Shiping Wen⁴, Kaibo Shi⁵, Yiqian Tang⁶

Affiliations

¹ School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu, 610106, China. Electronic address: shawion1980@163.com.
² State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610050, China. Electronic address: guoxiao@swpu.edu.cn.
³ College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu, 610050, China. Electronic address: atao596@163.com.
⁴ Centre for Artificial Intelligence, Faculty of Engineering Information Technology, University of Technology Sydney, Ultimo, NSW, 2007, Australia. Electronic address: shiping.wen@uts.edu.au.
⁵ School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu, 610106, China. Electronic address: skbs111@163.com.
⁶ School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu, 610106, China. Electronic address: tangyiqian@cdu.edu.cn.

PMID: 35970027
DOI: 10.1016/j.neunet.2022.07.031

Abstract

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.

Keywords: Bidirectional associative memory neural networks; Fractional-order neural networks; Octonion-valued neural networks; Synchronization.

MeSH terms

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Neural Networks, Computer*