Abstract: The symbiotic system of rural industrial revitalization comprises farming households, grassroots governments, and new rural collective economies as symbiotic units. The optimal symbiosis mode within this symbiotic system is reciprocal symbiosis. This study focuses on Yuhang District in Zhejiang Province, Yining County in Xinjiang Uygur Autonomous Region, and Wangcheng District in Hunan Province as research areas. Firstly, the grey Lotka-Volterra (GLV) model is employed to analyze the interaction within the current symbiotic system of rural industrial revitalization across these regions using data from 2019-2023. Secondly, this paper utilizes the GM(1,1) model to predict future data for these regions and analyze their future symbiosis. Subsequently, this paper examines the equilibrium point and stability of the symbiosis systems within these regions. Finally, based on an evolutionary game model approach, key factors influencing the evolution of a stable symbiosis system when satisfying and balancing interest demands among symbiotic units are explored. The findings reveal distinct characteristics within each subject's rural industrial revitalization symbiotic system. Government subsidies' intensity and cooperation benefits and costs primarily influence its evolution towards stability. 

Key words: Rural industrial revitalization, LV model, Symbiotic system, Evolutionary game