Grey Lotka-Volterra model for the co-evolution of technological innovation, resource consumption, environmental quality, and high-quality industrial development in Shaanxi Province, China.

The rapid industrialization and the lack of technological innovation over the past 40 years have caused serious environmental pollution and waste of resources. Therefore, it remains an urgent challenge to coordinate technological innovation, resource consumption, environmental quality, and high-quality industrial development in China. Using the data of Shaanxi Province from 2005 to 2019, in this paper, we adopt the 4-population grey Lotka-Volterra model (GLV) to study the competition and cooperation among technological innovation (TI), resource consumption (RE), environmental quality (EE), and industrial development quality (IQ). We also discuss the equilibrium point and stability of the GLV model and further verify its accuracy. We conduct an empirical study of the data of Shaanxi Province, and the results demonstrate that (1) TI is able to improve EE, increase IQ, and promote RE; (2) conserving resources has a positive effect on TI, EE, and IQ; (3) although EE could prevent TI and IQ, it can reduce RE; and (4) IQ can effectively reduce RE and improve EE; however, it hinders TI. (5) The result of equilibrium analysis reveals that the evolution of the four factors will tend to reach a stable equilibrium point in the future, that is, realizing co-evolution.