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

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.