The　dynamic　behavior　of　memristive　neural　networks　(MNNs),　including　synchronization,　effectively　keeps　the　robotic　stability　against　numerous　uncertainties　from　the　mimic　of　the　human　brain.　However,　it　is　challenging　to　perform　projective　quasi-synchronization　of　coupled　MNNs　with　low-consumer　control　devices.　This　is　partly　because　complete　synchronization　is　difficult　to　realize　under　various　projective　factors　and　parameter　mismatch.　This　article　aims　to　investigate　projective　quasi-synchronization　from　the　perspective　of　the　controller.　Here,　two　approaches　are　considered　to　find　the　event-triggered　scheme　for　lag　synchronization　of　coupled　MNNs.　In　the　first　approach,　the　projective　quasi-synchronization　issue　is　formulated　for　coupled　MNNs　for　the　first　time,　where　the　networks　are　combined　with　time-varying　delays　and　uncertainties　under　the　constraints　imposed　by　the　frequency　of　controller　updates　within　limited　system　communication　resources.　It　is　shown　that　our　methods　can　avoid　the　Zeno-behavior　under　the　newly　determined　triggered　functions.　In　the　second　approach,　following　classical　methods,　a　novel　projective　quasi-synchronization　criterion　that　combines　the　nonlinear　property　of　the　memristor　and　the　framework　of　Lyapunov-Krasovskii　functional　(LKF)　is　proposed.　Simulation　results　indicate　that　the　proposed　two　approaches　are　useful　for　coupled　MNNs,　and　they　have　less　control　cost　for　different　types　of　quasi-synchronization.　Copyright　©　2022　Yuan,　Luo,　Hu　and　Wang.