Haken-Entropy-Based Analysis of the Synergy Among Financial Support, Technological Innovation, and Industrial Upgrading

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.