Can voluntary environmental regulation play a major role in the transformation of traditional environmental regulation; undertake the task of improving the flexibility, autonomy, and effectiveness of environmental regulation; and promote green technology innovation of enterprises? This study uses the propensity score matching and difference-in-differences (PSM-DID) model to analyze the net effect and heterogeneity of voluntary environmental regulation on green technology innovation, and further explores the impact mechanism of voluntary environmental regulation on green technology innovation from three perspectives: government subsidies, public support, and external enterprise cooperation. The results show that voluntary environmental regulation has a significant positive effect on green technology innovation regardless of time, industry, and regional factors. The implementation of voluntary environmental regulation promotes the green patent authorization of enterprises by 15.12–17.59%. In addition, voluntary environmental regulation also shows industry heterogeneity, scale heterogeneity, and ownership heterogeneity for green technology innovation, and it emphasizes the promotion effect on enterprises in mild pollution industries, large-scale enterprises, and private enterprises. Furthermore, the implementation of voluntary environmental regulation will have a positive impact on green technology innovation by curbing public support and expanding cooperation with external enterprises.

This paper concerns the problem of fixed-time synchronization(FxS) of masterslave Lorenz systems. The adaptive control and fixed-time control strategies are successfully integrated so that not only the Lorenz systems can be synchronized within a fixed-time, but also the related controlling gains are not necessary to select beforehand.Distinguished from the conventional fixed-time control schemes, the proposed controller don't contain the signum function anymore, thereby the chattering behavior is avoided owing to its smoothness. The synchronizing condition is deduced according to the theory of fixed-time stability, and the upper bound of settling time is also estimated, which is irrelevant to the initial states of Lorenz systems. Apart from the correctness and effectiveness of theoretical analysis is validated by simulating Lorenz systems, the spirit of adaptive fixed-time control strategy is applied into synchronizing two finance systems finally.

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This paper concerns the problem of fixed-time synchronization(FxS) of master-slave Lorenz systems. The adaptive control and fixed-time control strategies are successfully integrated so that not only the Lorenz systems can be synchronized within a fixed-time, but also the related controlling gains are not necessary to select beforehand. Distinguished from the conventional fixed-time control schemes, the proposed controller don't contain the signum function anymore, thereby the chattering behavior is avoided owing to its smoothness. The synchronizing condition is deduced according to the theory of fixed-time stability, and the upper bound of settling time is also estimated, which is irrelevant to the initial states of Lorenz systems. Apart from the correctness and effectiveness of theoretical analysis is validated by simulating Lorenz systems, the spirit of adaptive fixed-time control strategy is applied into synchronizing two finance systems finally.

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