This article is concerned with the problem of finite-time mixed outer synchronization (FMOS) of complex networks with coupling time-varying delay. FMOS is a recently developed generalized synchronization concept, i.e., in which different state variables of the corresponding nodes can evolve into finite-time complete synchronization, finite-time anti-synchronization, and even amplitude finite-time death simultaneously for an appropriate choice of the controller gain matrix. Some novel stability criteria for the synchronization between drive and response complex networks with coupling time-varying delay are derived using the Lyapunov stability theory and linear matrix inequalities. And a simple linear state feedback synchronization controller is designed as a result. Numerical simulations for two coupled networks of modified Chua's circuits are then provided to demonstrate the effectiveness and feasibility of the proposed complex networks control and synchronization schemes and then compared with the proposed results and the previous schemes for accuracy.

As a typical technology-intensive industry, the renewable energy industry is a standard sample for scholars to study the R&D innovation of enterprises. At present, the industry is strongly supported by the government subsidy policy in China and has developed rapidly in recent years. Its own financing constraints and lack of innovation power are also the main problems for the development of renewable energy enterprises. Taking A-share renewable energy enterprises from 2016 to 2020 as the research object, this paper constructs a panel model to empirically study the relationship between government subsidies and enterprise innovation efficiency. The findings are as follows. First, government subsidies can significantly promote the innovation efficiency of enterprises; second, the government subsidy has an obvious double threshold effect on the innovation efficiency of enterprises, and when the government subsidy is in a certain range, the subsidy effect is the best; third, the government subsidy effect of non-state-owned renewable energy enterprises is better than that of state-owned enterprises; the effect of government subsidies for renewable energy enterprises in the central and western regions is better than that in the eastern region. The threshold effect of government subsidies on enterprise innovation efficiency is also quite different.

The synchronisation problem of complex networks with multiple coupled time-varying delays is investigated in this paper. By using Lyapunov stability theory and robust adaptive principle, several synchronisation criteria are deduced for both complex networks with and without norm uncertainties. The main results show that the states of all nodes of complex networks globally asymptotically synchronise to a desired synchronisation state by designing suitable robust adaptive synchronisation controllers which have strong robustness against the uncertainties in coupling matrices. Finally, several illustrative examples with numerical simulations are given to show the feasibility and robustness of theoretical results.