Fixed-Time Synchronization of Impulsive Octonion-Valued Fuzzy Inertial Neural Networks via Improving Fixed-Time Stability

A model of impulsive octonion-valued fuzzy inertial neural networks (OVFINNs) with time-varying delays is established, and fixed-time (FXT) synchronization is investigated by using direct octonion approach. First, a new FXT stability lemma of impulsive systems is presented and the upper bound of settling time is estimated by using the average impulsive interval and comparison principle. Second, two inequalities on fuzzy logic are developed in the field of octonion. Third, novel lemmas are introduced based on octonion-valued norm and sign function to overcome the non associative and non commutative laws of octonion multiplication. Furthermore, two new nonlinear octonion-valued controllers are directly designed to induce the FXT synchronization. Then, according to the improving FXT stability lemma and designed controllers, some novel sufficient conditions are given to ensure FXT synchronization of OVFINNs. Finally, two numerical simulations are given to demonstrate the correctness of the theoretical results and the effectiveness of FXT synchronization in secure communication.