Fixed-Time Synchronization Analysis for Complex-Valued Neural Networks via a New Fixed-Time Stability Theorem

Based on variable substitution, calculating definite integral and solving the minimization problem, in this paper we establish a new fixed-time stability theorem, which can provide a novel upper bound estimate formula for the settling time. By dividing the considered complex-valued neural networks (CVNNs) into double-layer real-valued neural networks, the fixed-time synchronization of CVNNs is analyzed by means of the new fixed-time stability theorem. Both theoretical derivation and numerical simulation show the new upper bound estimate formula for the settling time in this paper is more accurate than that given in the classic fixed-time stability theorem. A numerical example is given to verify the effectiveness of the main results.