To analyze the impact of interaction size on cooperation level and population average payoff in the public goods game with punishment, by combining Monte Carlo simulation with the characteristics of real complex interaction environments, a dynamic interaction domain model was proposed based on a cooperation threshold. First, a dynamic interaction rule based on the cooperation threshold is designed, taking into account the characteristics of different numbers of cooperators in the game group. Secondly, simulation experiments are conducted to observe the evolution of cooperation level, population payoff, and interaction domain range in the public goods game model after incorporating the interaction domain update rule. Finally, we compare the effects of the traditional and new models on the evolution of cooperation under different parameter values and discuss the principles and effectiveness of the model. Extensive simulation experiments have validated that increasing the cooperation threshold or the variation parameter more efficaciously fosters cooperation and enhances the population's average payoff.This provides a new perspective for the study of public goods game in dynamic interactive environment.