The fractal characteristics and risk indicators of urban ecological environment vulnerability evolution

Abstract

Exploring whether the evolution system of urban ecological environment vulnerability had fractal characteristics is an important basis for objectively evaluating the risk of urban ecological environment vulnerability and improving the reliability of risk warning. Existing research focused on explaining the performance characteristics of complex systems through single scale and multi-dimensional features, and could not dynamically depict the infinite fine approximation characteristics between local development and overall situation of complex systems, resulting in weak reliability of urban ecological environment vulnerability risk warning. Introducing fractal theory into the study of the characteristics of urban ecological environment vulnerability systems, a systematic framework for judging the fractal characteristics of urban ecological environment vulnerability evolution was established around the nonlinear, long-range correlation, and scale-free aspects of fractal theory. Based on the 20 years panel data of 35 cities in China, the fractal characteristics of urban ecological environment vulnerability systems were verified, and the relationship between Hurst index and fractal dimension in continuous time windows was further established. The complexity of urban ecological environment vulnerability systems in continuous time windows was accurately characterized by fractal dimension, providing effective indicators for risk assessment. The results showed that the vulnerability evolution system of urban ecological environment had complexed nonlinear characteristics, and the random Hurst indexes calculated by rescaled range analysis (R/S) was close to 0.5, indicating that the vulnerability evolution system had long-term memory. The vulnerability evolution system described by the random walk model follows a power-law relationship, indicating that the vulnerability evolution system had scale-free self-similarity characteristics. The risk level of the vulnerability evolution system described by the fractal dimension is consistent with reality, indicating that the fractal dimension had strong indicative effect on the risk judgment of the vulnerability evolution system.