This paper investigates the exponential stability of a class of neutral inertial neural networks with multi-proportional delays and leakage delays. By utilizing the Lyapunov stability theory, the approach of parametric variation, and the differential inequality technique, some criteria are acquired that can guarantee that all solutions of the addressed system converge exponentially to the equilibrium point. In particular, the neutral term, multi-proportional delays, and leakage delays are incorporated simultaneously, resulting in a more general model, and the findings are novel and refine the previous works. Finally, one example is provided to indicate that the dynamic behavior is consistent with the theoretical analysis.

As an essential dynamic behavior, the synchronization of inertial Cohen–Grossberg neural networks (ICGNNs) has received considerable attention due to its successful applications in neural cryptography, public channel cryptography, security communications, and image encryption. In this article, the $\alpha$-synchronization of a class of non-autonomous unbounded delayed inertial Cohen–Gossberg neural networks with delayed impulses is investigated. Firstly, several non-autonomous impulsive differential inequalities are established, where unbounded delays, delayed impulses, and time-variable coefficients are incorporated. Subsequently, based on the proposed impulsive differential inequalities and Lyapunov function approach, the feedback controllers are designed, and some criteria for $\alpha$-synchronization are provided. Finally, the validity of the presented theoretical findings is demonstrated by two specific examples. It is shown that delayed impulses can be viewed as perturbations or stabilizing sources for non-autonomous ICGNNs.