The convergence of China’s digital economy and green finance holds great significance for fostering a sustainable and high-quality developmental path. However, existing studies have not explored the coupling coordination development between these two crucial subsystems. To bridge this gap, this paper employs a modified coupling coordination degree (CCD) model to assess and affirm the coupling coordination degree between the digital economy and green finance across 30 provinces in China from 2015–2021. Based on degree results, provinces are classified into three clusters by using K-means and hierarchical clustering algorithm. Our findings unveil that the current level of coupling coordination development in China is at a primary coordination stage. Although regional disparities significantly exist, the overall level of coordination remains steadily increasing, with the eastern region outperforming the western region. Additionally, we determine that the COVID-19 pandemic’s disruption on the coupling coordination development of these systems has been limited. This research sheds light on the evolution of coupling systems and offers practical recommendations for strengthening the coordinated development of the digital economy and green finance.

Existing studies predominantly explore the link between green finance and ecological environment but overlook their dynamic spatiotemporal evolution and regional disparities. This study optimizes the coupling coordination degree (CCD) model and employs methods such as the Dagum This study innovates by optimizing the CCD model and integrating spatial econometrics with dynamic distribution methodologies to measure the coupling coordination dynamics in China from 2013 to 2022. Findings reveal an overall upward trend but significant regional disparities. The Eastern region exhibits a “high-high” clustering effect, while the Central and Western regions face a “low-low” lock-in, reflecting a “Matthew effect.” Green innovation and environmental governance improve coordination level, whereas resource consumption hinders it, with varying regional impacts. These insights inform targeted strategies, emphasizing regional cooperation and innovation-driven policies for balanced development.

In this paper, an integral sliding mode controller is proposed to realize the synchroniza-tion of a class of finance chaotic systems. First, an integral sliding surface with tanh function is designed. Then, fuzzy logic systems are used to estimate unknown functions, and then based on the Lyapunov stability theorem, the proposed control method can quickly drive the synchroniza-tion error into a small neighborhood of zero, and the range of this neighborhood can be estimated. The simulation results verify that the proposed method in this paper is better than the traditional method.