Symbiotic evolution in regional green innovation ecosystems: A Lotka-Volterra model analysis of China's provincial

The development of the regional green innovation ecosystem (RGIE) can boost the global economy and mitigate environmental risks. However, RGIE exhibits significant heterogeneity in actor interactions, resource allocation, and evolutionary pathways. This study integrates symbiosis theory to construct a tripartite RGIE framework involving the government (GOV), enterprises (ENT), and academic institutions (ACD), and applies the Lotka-Volterra model to qualitatively and quantitatively analyze the symbiotic relationships of RGIE in 30 provinces in China. The findings reveal that: (1) The symbiotic relationships primarily present three patterns: mutualism, parasitism, and competition. GOV-ENT primarily exhibits mutualistic symbiosis, GOV-ACD primarily shows parasitism, and ENT-ACD predominantly demonstrates competitive symbiosis. (2) Mutualistic symbiosis can maximize the development of t RGIE, while parasitic and competitive symbioses may lead to system instability or insufficient innovation drive. (3) Regional resource endowments and institutional environments shape the symbiotic paths. Coastal areas are more likely to achieve mutualistic equilibrium due to market-based coordination, whereas central and western regions are trapped in parasitic lock-ins due to resource misallocation. Based on these findings, differentiated policy tools are proposed: implementing green patent revenue feedback mechanisms in mutually beneficial regions, promoting green performance-based agreements in parasitic regions, and designing resource quota trading markets in competitive regions. This study provides empirical support for the government in formulating precise green innovation policies through the interdisciplinary integration of ecological models and policy design, and offers insights for the global optimization of green innovation ecosystems.