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Global stability analysis of fractional-order quaternion-valued bidirectional associative memory neural networks

Humphries, Usa, Rajchakit, Grienggrai, Kaewmesri, Pramet, Chanthorn, Pharunyou, Sriraman, Ramalingam, Samidurai, Rajendran and Lim, Chee Peng 2020, Global stability analysis of fractional-order quaternion-valued bidirectional associative memory neural networks, Mathematics, vol. 8, no. 5, pp. 1-27, doi: 10.3390/MATH8050801.

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Title Global stability analysis of fractional-order quaternion-valued bidirectional associative memory neural networks
Author(s) Humphries, Usa
Rajchakit, Grienggrai
Kaewmesri, Pramet
Chanthorn, Pharunyou
Sriraman, Ramalingam
Samidurai, Rajendran
Lim, Chee PengORCID iD for Lim, Chee Peng orcid.org/0000-0003-4191-9083
Journal name Mathematics
Volume number 8
Issue number 5
Article ID 801
Start page 1
End page 27
Total pages 27
Publisher MDPI AG
Place of publication Basel, Switzerland
Publication date 2020-05
ISSN 2227-7390
Keyword(s) global asymptotic stability
fractional-order
quaternion-valued
bidirectional associative memory
linear matrix inequality
Summary We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results.
Language eng
DOI 10.3390/MATH8050801
Indigenous content off
HERDC Research category C1 Refereed article in a scholarly journal
Persistent URL http://hdl.handle.net/10536/DRO/DU:30138781

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Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.