New energy vehicle industry is an important strategic emerging industry for cultivating national new quality productivity with high-tech, high-efficiency and high-quality characteristics. Based on patent application data during 2013-2022 of the three leading enterprises (BYD, GEELY and WULING), Lotka-Volterra population competition model is constructed to explore out their coopetition relation mode and evolving trends. Detailed references are supplied for optimizing innovation allocation and accelerating more high-quality innovation fruit breakthrough. Main conclusions are as follows. Firstly, Lotka-Volterra population competition model shows higher goodness, when coopetition relation among enterprises is under consideration. Coopetition relation has been an important driving factor to stimulate technological innovation evolution. Secondly, their coopetition model shows great heterogeneity among the three leading enterprises. At current stage, “BYD + GEELY”、“WULING + GEELY” show such mutually promoting type. Meanwhile, “ BYD +WULING” show the competition-cooperation type. Thirdly, in accordance with simulation results, innovation outputs of enterprises vary with coopetition relation coefficient changes. Innovation output effect of new vehicle industry is positive when the coopetition intensity of mutually-prompting type grows. The positive innovation effect from “WULING + GEELY” coopetition intensity growth is more than that from the other one. Therefore, cultivating orderly competition and coordinated cooperation mode mechanism, especially most potential competition types, should be paid more focus on realizing its high-quality innovation outputs and supporting its new-quality productivity formation for the new energy vehicle industry of China.