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

• Main Authors: Usa Humphries, Grienggrai Rajchakit, Pramet Kaewmesri, Pharunyou Chanthorn, Ramalingam Sriraman, Rajendran Samidurai, Chee Peng Lim
• Format: Journal
• Published: 2020
• Subjects: Mathematics
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85086664222&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/70716
• Institution: Chiang Mai University

© 2020 by the authors. 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 Ito'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.