<p>This paper focuses on addressing the synchronization issue of inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) under hybrid cyber attacks. First, hybrid cyber-attacks in network communications are considered, highlighting the variety of attack strategies and the uncertainties inherent in their occurrence and impact. Second, an aperiodic quantized sampled-data (AQSD) controller is proposed to address the limited transmission capacity in network communications. In addition, an asymmetric Lyapunov–Krasovskii functional (LKF) method and looped-functional terms are introduced to further relax the initial constraints requirement. Next, less conservative synchronization criteria for the drive–response systems are deduced. Finally, numerical simulation is used to demonstrate the effectiveness and superiority of the proposed method.</p>