Evolutionary Analysis of Innovation Development in a Metropolitan Area from a Symbiosis Perspective: Empirical Research on the Shanghai Metropolitan Area

Promoting the innovative development of cities in the metropolitan area holds great significance for China's implementation of the "innovation-driven development" strategy. According to symbiosis theory, this paper constructed a city-based Lotka-Volterra symbiosis model and innovation-level index system. We used the Shanghai metropolitan area as a sample for empirical analysis to explore the evolution of the comprehensive development level of urban innovation under different symbiotic relationships. The research results showed that under a reciprocal relationship, the innovative development of core city and node cities was higher than the actual level; under a mutual inhibition symbiosis or parasitic symbiotic relationship, the innovative development of core city and node cities was lower than the actual level; and under an independent symbiotic relationship, the innovative development of the core city was higher than the actual level, while that of the node cities was lower than the actual level.