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.

We studied the problem of accuracy-preassigned finite-time exponential synchronization of neutral-type Cohen–Grossberg memristive neural networks involving time-varying multiple leakage and transmission delays. First, a novel method was presented to give an estimation formula for solutions of the error system. Then, the estimation formula was used to establish sufficient conditions guaranteeing accuracy-preassigned finite-time exponential synchronization of the considered memristive Cohen–Grossberg neural networks. The obtained sufficient conditions were composed of some linear scalar inequalities that was easy to solve by employing standard tool softwares. Moreover, the approach proposed here was based on the concept of accuracy-preassigned finite-time exponential synchronization, and Lyapunov–Krasovskii functionals or model transformations were not involved, simplifying the theorematic proof. Finally, two numerical examples were given to present the validity of theorematic 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.