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

Year: 2020
Type: article
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.
Source: Mathematics
DOI: 10.3390/math8050815
Authors: Usa Humphries, Grienggrai Rajchakit, Pramet Kaewmesri, Pharunyou Chanthorn, Ramalingam Sriraman, Rajendran Samidurai, Chee Peng Lim
Institutions: King Mongkut's University of Technology Thonburi, Maejo University, Chiang Mai University, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Thiruvalluvar University, Deakin University
Language: English
Open Access status: gold
Estimated APC paid: $1,267
OpenAlex ID: W3024378632
FWCI: 4.61
Cites: 41
Cited by: 47
Related to: 10