Stability Analysis of Green Manufacturing Innovation Ecosystem Based on Symbiotic Stochastic Evolutionary Game

In the modern era, the green manufacturing innovation ecosystem is vital for promoting sustainable development. It significantly contributes to achieving carbon peak and carbon neutrality goals. Current research regarding the coevolution of the green manufacturing innovation ecosystem predominantly utilizes deterministic models. These models do not account for the inherent stochasticity present in interactions within the innovation ecosystem, and they also neglect quantitative analyses pertaining to ecosystem resilience and stability mechanisms. This study explores the core mechanisms that drive the stability of the green manufacturing innovation ecosystem. It is based on theories of ecology and innovation. This study employs the Lotka–Volterra model to characterize the stochastic evolutionary process of symbiotic interactions among innovation groups. Compared to deterministic models, the stochastic approach has significant advantages. It captures the inherent uncertainties of human behavior and subjective decision-making. Additionally, it accounts for dynamic environmental changes. This approach provides more realistic insights into the evolution of green manufacturing innovation ecosystems amid complex conditions. The findings yield three key conclusions. First, the mutualistic symbiosis model is more stable than other models. This includes independent, competitive, parasitic, and commensal symbiosis models. This stability underscores the mutualistic model’s critical role in sustaining the ecosystem’s development. Second, the return time for a mutualistic symbiosis ecosystem is notably shorter than for a stochastic interaction ecosystem. This indicates that mutualistic symbiosis is more effective in fostering growth within the green manufacturing innovation ecosystem. Third, participant relationships in this ecosystem are complex. They encompass competitive, parasitic, and commensal dynamics, among others. Furthermore, the ecosystem’s resilience improves as the rate of mutually beneficial interactions increases. These findings provide direct policy and management guidance for optimizing the symbiotic mechanisms of green manufacturing innovation ecosystems, enhancing ecosystem resilience, and advancing carbon peaking and carbon neutrality goals.