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. Attached Files Name Description MIMEType Size Downloads lim-stochasticmemristive-2020.pdf Published version application/pdf 563.27KB 63 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 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 Persistent URL http://hdl.handle.net/10536/DRO/DU:30139804 Document type: Journal Article Collections: Institute for Frontier Materials Open Access Collection GTP Research Related Links Link Description Link to full-text (open access)     Unless expressly stated otherwise, the copyright for items in DRO is owned by the author, with all rights reserved. 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. Versions Version Filter Type Fri, 10 Jul 2020, 14:32:27 EST Sat, 11 Jul 2020, 05:00:53 EST Mon, 13 Jul 2020, 08:06:04 EST Thu, 20 Aug 2020, 06:02:51 EST Mon, 31 Aug 2020, 16:37:31 EST Mon, 31 Aug 2020, 16:41:41 EST Filtered Full Citation counts:   Cited 0 times in TR Web of Science Cited 4 times in Scopus Search Google Scholar Access Statistics: 88 Abstract Views, 63 File Downloads  -  Detailed Statistics Created: Fri, 10 Jul 2020, 14:32:27 EST

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