Stability of stochastic Hopfield neural networks driven by [formula omitted]-Brownian motion with time-varying and distributed delays

Abstract

In this paper, pth exponential stability and quasi-surely exponential stability of stochastic Hopfield neural 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.