Agricultural modernization needs to change the traditional production mode, while the technology diffusion for green agriculture is an important way to realize the change. This paper constructed an asymmetric evolutionary game model, between “government-farmers”, that analyzes the strategy evolution path of each game subject and the factors affecting its strategy evolution, by using the stability theory of a differential equation, and discusses the stability strategy of the system by using the Jacobian matrix. In part of numerical simulation, the interactive evolution-path between the government and farmers in agricultural green technology extension is analyzed; and the influence of government penalties, purchasing costs of green technology; gains from green products and other variables, on the stability strategy of evolutionary systems, are simulated when government penalties are greater than the sum of supervision fees and agricultural subsidies. Research shows that increasing government subsidies for green production, and government penalties for non-green production, can encourage farmers to adopt green production methods which is conducive to the diffusion of green technology. The need to promote this technology is only necessary if the profits obtained by farmers, with green production technology, are higher than a certain threshold; otherwise, this will make it difficult to promote the technology.
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