This paper studies the global exponential stability problem of quaternion-valued neural networks (QVNNs) with leakage, transmission, and distribution delays. To address this issue, a direct method based on system solutions is proposed to ensure the global exponential stability of the considered network models. In addition, this method does not need to construct any Lyapunov-Krasovskii functional, which greatly reduces the amount of computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.

This work established synchronization criteria for master-slave inertial neural networks with leakage time-varying delays and proportional delays, The solution employed a direct analysis method based on parameterized system solutions. The derived synchronization conditions consisted of only a few simple inequalities, which were easy to solve.Based on the adopted approach, a novel class of synchronization controllers was designed for proportional delays without constructing any complex functionals. Using the proposed method, leakage delays could be transformed into their maximum absolute values, enabling the derivation of delay-dependent conditions without any intricate treatment of leakage delays. Furthermore, it was noteworthy that this paper presented the first investigation into this problem using the proposed method, and the technique employed was novel. Finally, numerical simulations were provided to verify the effectiveness of the proposed method.