Finite-time Stepanov almost periodic synchronization for fractional-order stochastic high-order Hopfield neural networks

This paper investigates the dynamics of high-order Hopfield neural networks incorporating fractional-order derivatives, stochastic disturbances, and time-varying delays. To address the more realistic scenario of discontinuous or weakly regular time-varying parameters, the analysis is conducted within the framework of Stepanov almost-periodicity. First, sufficient criteria for the existence and uniqueness of a Stepanov almost periodic solution in distribution for the considered network are established using Banach's fixed point theorem and inequality techniques. Subsequently, by treating the studied network as a drive system, a corresponding response system is constructed. Effective control strategies are designed to achieve finite-time synchronization between these two systems. Finally, a numerical example is provided to illustrate the validity of the theoretical results. This study offers new theoretical insights for analyzing almost periodic oscillations in complex fractional-order stochastic systems with delays and has potential applications in fields requiring precise temporal coordination, such as secure communication and cooperative control.