Almost periodic dynamics of fractional-order stochastic Hopfield neural networks with time-varying delays

Although fractional-order stochastic neural networks exhibit rich dynamics, there are currently no research results on their almost periodic dynamics in the sense of distribution. This paper investigated a class of fractional-order stochastic Hopfield neural networks with time-varying delays. By employing the Banach fixed point theorem and inequality techniques, we first established sufficient criteria for the existence and uniqueness of almost periodic solutions in distribution for the considered model. Subsequently, through the application of a generalized Gronwall inequality, the finite-time stability in the mean square sense of this unique almost periodic solution in distribution was rigorously demonstrated. The results obtained in this study are entirely novel. To validate the theoretical findings, a numerical example with explicit parameters was constructed for simulation verification, where computational results exhibit a high degree of consistency with theoretical derivations.