Abstract: At present, to accelerate the upgrading of industrial structure and the demand of forming new economic growth point, governments of most countries are urged to launch various optimized subsidy policies to support the development of new energy automobile industry. In the application process of subsidy policies for new energy automobile industry, there are both cases of research and development (R&D) subsidies or market subsidies acting alone, also cases where there are mixed subsidies at the same time. So, what impact does R&D subsidies have on R&D investment of new energy auto companies, and what is the effect on market stability? Can market subsidies stimulate the R&D investment of new energy auto companies and maintain market stability? What effect will the mixed subsidies of R&D and market have on the new energy automobile industry? What are the characteristics of each of the R&D subsidy market subsidies, and how should the subsidy method be selected? These issues are worthy of discussion. In view of the above, a dynamic game model based on the branch theory of dynamic system is constructed, and the effects of three new energy vehicle subsidies on market stability are discussed, including:1) research and development (R&D) subsidies; 2) market subsidies; 3) mixed subsidies. The results show that:firstly, new energy vehicle R&D subsidies can stimulate R&D investment, but the increase of subsidies will reduce market stability; Secondly, the incentive effect of new energy vehicle market subsidy on R&D investment is weaker than that of R&D subsidy; Finally, under the mixed subsidies of new energy vehicles, the incentive effect of R&D subsidies on the R&D investment of enterprises is better than that of market subsidies, the incentive effect on the profits of enterprises is worse than that of market subsidies, and the improvement of market stability of new energy vehicles is better than that of market subsidies. Based on this, it is suggested that the Backward slope of market subsidy should be reduced, and in the future we should carry out "R&D investment interval gradient subsidy" corresponding with the R&D investment of NEV enterprises, in order to reduce the adjustment speed of R&D investment, increase the market stability and promote the development of new energy automobile industry. The research conclusions of this paper provide a theoretical basis for reference based on enterprise R&D investment, industrial development, market stability, and improvement of new energy vehicle subsidies for regional characteristics and industrial development stages.In addition, the R&D investment is adjusted dynamically according to the profit signal, and the dynamic system branch and the chaotic bifurcation theory are applied to explain the relevant policy implications. If you further relax or change the relevant assumptions, you may get some new conclusions.

Key words: new energy vehicles, dynamic game, government subsidies, R&D investment