Launch an In-Aepth Analysis on the Global Mittag Leffler Synchronization Problem of Fractional-Order Octonion-Valued Fuzzy BAM Neural Networks

This paper proposes a novel class of fractional-order octonion-valued fuzzy bidirectional associative memory neural networks (FOOVFBAMNNs). To address the analytical challenges arising from the inherent nonassociativity and noncommutativity of octonion algebra, we employ the Cayley–Dickson construction to decompose the original octonion-valued system into four coupled fractional-order complex-valued subsystems. Two inequalities are established in the complex-valued fuzzy logic domain, which are specifically tailored to handle complex-valued activation functions, connection weights, and state variables, providing tighter bounds for synchronization criterion derivation. A simple yet effective linear feedback controller and a properly constructed Lyapunov–Krasovskii functional (LKF) are designed for the transformed complex-valued error systems. By integrating fractional-order Lyapunov stability theory with the proposed inequalities, we derive sufficient conditions for global Mittag-Leffler synchronization of FOOVFBAMNNs under both general activation functions and linear threshold activation functions. Numerical simulations are conducted to verify the correctness and effectiveness of the obtained theoretical results.