<p>This paper concentrates on the study of passivity-based synchronization of inertial neural networks including Markov jump parameters. The second-order differential equations are converted into first-order differential equations using the variable transformation method. To make effective use of network bandwidth resources and to optimize the Markov jump inertial neural networks (MJINNs) performance, an adaptive event-driven protocol controller is studied. To achieve synchronization, an appropriate Lyapunov-Krasovskii functional (LKF) is constructed, which includes double integral terms that capture the information of time-varying delay terms. Some sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) using Reciprocal convex combination lemma (RCCL). Then, a numerical simulation and an application of image encryption are carried out to illustrate the effectiveness of the proposed method.</p>