The paper uses the panel smooth conversion fractional-order system model to divide the mechanism of financial development in high-tech industries into two systems. At the same time, the article uses a continuous state to connect these two extreme situations to investigate the nonlinear characteristics of linear feedback control that inhibit the impact of financial development on high-tech industries. Studies have shown that financial development under a low system has a significant role in promoting high-tech industries. On the other hand, financial development under the high-level system has a restraining effect on high-tech industries. There are dual-threshold characteristics between the scale of financial development and the development of high-tech industries. Firstly, the scale of financial development should be controlled within [0.553, 0.840]. Secondly, there is a single threshold between the level of financial development and the development of high-tech industries, and the level of financial development should be controlled within 0.756.
Keywords: PSTR; financial development; fractional financial system; high-tech industry; linear feedback; nonlinear.