Technological innovation, the financial market, and the real economy are mutually promoting and restricting. Considering the interference of market-noise information, this paper applies the wavelet-denoising method of the soft- and hard-threshold compromise functions to process the original information so as to eliminate the noise information, and combines multifractal detrended cross-correlation analysis with the sliding-window approach, focusing on the change in the Hurst index and the parameter change in the multifractal spectrum to explore the interaction in between. The research results show that there is a certain cross-correlation among technological-innovation, financial-market, and real-economy indices. Firstly, the cross-correlation among them has significant multifractal characteristics rather than single-fractal characteristics. Secondly, the fractal characteristics reveal the long memory of the interaction among the three indices. Thirdly, there are also obvious differences in the degree of local chaos and volatility of the interaction. Fourthly, the cross-correlation among technological-innovation, financial-market, and real-economy indices has significant multifractal characteristics rather than single-fractal characteristics. In comparison, the cross-correlation multifractal characteristics among technological innovation, the financial market, and the real economy are time-varying, and the cross-correlation multifractal characteristics between the technological-innovation index and the real-economy index are the most obvious.

This study reveals the internal mechanism of the synergetic evolution of financial support, technological innovation, and industrial upgrading from the perspective of system synergy. It aims to provide a theoretical basis and reference for promoting benign interactions among these elements, thereby driving high-quality economic development. During the research process, an evaluation indicator system was constructed based on China’s industrial development data, utilizing the entropy method to determine indicator weights and the Haken model to analyze synergy effects. In a methodological innovation, this study identifies the system’s order parameters to derive the potential function. Through this approach, it systematically analyzes the dynamic evolution characteristics and synergetic mechanisms of the composite system. The research results indicate that the three systems have formed a mutually promoting and closely coupled compound synergetic mechanism, rather than following a single linear transmission path. The overall synergy level presents a medium-to-low development trend, following an asymmetric U-shaped evolution trajectory that first decreases and then slowly recovers. Furthermore, the degree of synergy exhibits an inverse relationship with the volatility of the subsystems, suggesting that the stability of synergy is highly susceptible to external forces and remains in a state of dynamic flux.