期刊论文详细信息
Mathematics
Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability
Pramet Kaewmesri1  Usa Humphries1  Grienggrai Rajchakit2  Rajendran Samidurai3  Ramalingam Sriraman4  CheePeng Lim5  Pharunyou Chanthorn6 
[1] Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru 10140, Thailand;Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand;Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu-632115, India;Department of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Tamil Nadu-600 062, India;Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia;Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand;
关键词: stochastic memristive quaternion-valued neural networks;    exponential input-to-state stability;    Lyapunov fractional;   
DOI  :  10.3390/math8050815
来源: DOAJ
【 摘 要 】

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.

【 授权许可】

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