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Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability

Usa Humphries (), Grienggrai Rajchakit (), Pramet Kaewmesri (), Pharunyou Chanthorn (), Ramalingam Sriraman (), Rajendran Samidurai () and Chee Peng Lim ()
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Usa Humphries: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru 10140, Thailand
Grienggrai Rajchakit: Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand
Pramet Kaewmesri: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru 10140, Thailand
Pharunyou Chanthorn: Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Ramalingam Sriraman: Department of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Tamil Nadu 600 062, India
Rajendran Samidurai: Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu 632115, India
Chee Peng Lim: Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia

Mathematics, 2020, vol. 8, issue 5, 1-26

Abstract: 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 It o ^ ’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.

Keywords: stochastic memristive quaternion-valued neural networks; exponential input-to-state stability; Lyapunov fractional (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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