Almost Periodic Uniform Stability of Delayed Fractional-Order Quaternion-Valued Fuzzy Neural Networks with Stochastic Terms Via a Direct Method

Abstract

Fractional-order neural networks are vital for modeling neuronal interactions in information processing, and exploring their existence and stability remains a key research challenge. This paper aims to achieve almost periodic uniform stability for fractional-order stochastic fuzzy neural networks in the quaternion field, which is crucial for ensuring reliable and sustained periodic performance in dynamic environments, essential for applications like simulating biological neural systems. We employ a direct method without decomposing quaternion-valued networks into real-valued counterparts, and by leveraging fixed point theorem, fundamental fractional calculus properties, and various inequality techniques, we establish the existence of a unique almost periodic solution under specific conditions. Additionally, by constructing an error system and applying uniform stability definitions with inequality methods, we derive conditions for almost periodic uniform stability. Finally, MATLAB simulations validate the feasibility and accuracy of our results.