Collaborative evolution of regional green innovation system under the influence of high-speed rail based on Belousov-Zhabotinsky reaction

As a green transportation mode and carrying factors with high knowledge-intensive characteristics, high-speed rail (HSR) has contributed to the improvement of regional green innovation. However, the relationship between HSR and regional green innovation is still limited. Based on the Belousov-Zhabotinsky (B-Z) reaction model, this study establishes a three-dimensional logistic dynamic evolution model for factor flow, knowledge spillover and green innovation performance. Through linear stability analysis, the threshold conditions for the evolution of the regional green innovation system under the influence of HSR are explored, and the impact of HSR policy on the regional green innovation system under four different initial states is examined. The results reveal four major points: (1) Factor flow is the order parameter and shows a significant collaborative relationship with green innovation performance. (2) The opening of HSR can effectively promote the evolution of the regional green innovation system, and the powerful stimulus of HSR contributes to shortening its evolutionary cycle. (3) The initial state of the regional green innovation system plays a crucial role in the green innovation performance. (4) In the process of collaborative evolution of regional green innovation system, factor flow and knowledge spillover serve as the premise and foundation, respectively, to jointly promote green innovation performance enhancement. Findings not only provide references for decision-makers to implement green innovation strategy and boost the green innovation performance, but also extend the theoretical system of HSR effect and collaborative evolution.