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Stochastic memristive quaternion-valued neural networks with time delays: An analysis on mean square exponential input-to-state stability

Humphries, Usa, Rajchakit, Grienggrai, Kaewmesri, Pramet, Chanthorn, Pharunyou, Sriraman, Ramalingam, Samidurai, Rajendran and Lim, Chee Peng 2020, Stochastic memristive quaternion-valued neural networks with time delays: An analysis on mean square exponential input-to-state stability, Mathematics, vol. 8, no. 5, pp. 1-26, doi: 10.3390/MATH8050815.

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Title Stochastic memristive quaternion-valued neural networks with time delays: An analysis on mean square exponential input-to-state stability
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 815
Start page 1
End page 26
Total pages 26
Publisher MDPI
Place of publication Basel, Switzerland
Publication date 2020-05-18
ISSN 2227-7390
Keyword(s) stochastic memristive quaternion-valued neural networks
exponential input-to-state stability
Lyapunov fractional
Summary In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying Itoˆ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.
Language eng
DOI 10.3390/MATH8050815
Indigenous content off
Copyright notice ©2020, the authors
Free to Read? Yes
Use Rights Creative Commons Attribution licence
Persistent URL http://hdl.handle.net/10536/DRO/DU:30139804

Document type: Journal Article
Collections: Institute for Frontier Materials
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