Credit problems are the main bottleneck in the development of e-commerce. Both the time and degree of e-commerce credit control directly affect its economic benefits. From the perspective of the criticality of complex systems, this paper explores the control node of e-commerce credit behaviour. Implementing control in this node can not only ensure the stable development of the credit network but also optimise the control cost. This paper constructs a credit behaviour model for the four regulatory behaviours of the transaction subject, analyses the evolution law of the credit network, and determines the critical state of the network. Finally, the paper’s empirical analysis and simulation experiments prove that when the false information in the credit network in the empirical data is 32%, the implementation of credit control has an efficient control effect. Nevertheless, 32% is not a universal result; the specific critical point value needs to be recalculated according to the theoretical derivation of the critical point combined with the actual network. These research results can help regulators obtain the highest regulatory return with the lowest regulatory investment.

The finite-time pinning synchronization control problem is studied for coupled complex networks with time-varying delays. Based on the finite-time stability theorem, a finite-time tractive synchronous controller is designed. In addition, the selection process of tractive nodes is developed to control as few nodes as possible such that all nodes are synchronized in the network in finite time. At the same time, sufficient conditions of the finite-time constraint synchronization of the drive-response network are obtained using the Lyapunov stability theory and the matrix inequality method. The effectiveness of the proposed controller is verified by numerical simulation. This approach can be applied to large-scale complex networks with time-varying delays.