Stability of stochastic Hopfield neural networks driven by G-Brownian motion with time-varying and distributed delays

In this paper, pth exponential stability and quasi-surely exponential stability of stochastic Hopfield neu-ral networks driven by G-Brownian motion are investigated. Under a sublinear expectation framework, we give several lemmas related to the Halanay inequality and the Burkholder-Davis-Gundy ineqaulity. Our stability results is based on the class of the multidimensional Halanay inequalities, as well as the Burkholder-Davis-Gundy inequalities. The main originality lies in the fact that we consider Knightian uncertainty of the theory model of stochastic Hopfield neural networks. Finally, two numerical examples are presented to illustrate our new theory.(c) 2022 Published by Elsevier B.V.

Automated summary

In this paper, the pth exponential stability and quasi-surely exponential stability of stochastic Hopfield neural networks driven by G-Brownian motion are investigated. Several lemmas related to the Halanay inequality and the Burkholder-Davis-Gundy inequality are given under a sublinear expectation framework. The main originality lies in considering the Knightian uncertainty of the theory model. Numerical examples are presented to illustrate the new theory.