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Article summary:

1. Pinning control is an important strategy for controlling large ensembles of interacting units.

2. This paper investigates the pinning adaptive synchronization of complex multi-links networks by utilizing Lyapunov stability theory.

3. The paper evaluates the number of nodes needed to be pinned in multi-links networks, the effect of time-delay on the whole network, and the suitable coupling strength to control the network with a certain number of pinning controllers.

Article analysis:

The article provides a comprehensive overview of pinning adaptive synchronization of complex dynamical networks with multi-links, and presents several criteria for achieving this goal. The authors provide mathematical proof to evaluate the number of nodes needed to be pinned in multi-links networks, as well as the effect of time-delay on the whole network and suitable coupling strength to control it with a certain number of pinning controllers. The article also provides numerical examples for illustrating synchronization, which are useful for understanding how these criteria can be applied in practice.

The article is generally reliable and trustworthy, as it is based on established research findings and provides evidence to support its claims. However, there are some potential biases that should be noted. For example, while the authors discuss possible applications for their findings (e.g., social network control, advertising), they do not explore any potential risks associated with these applications or consider any counterarguments that may exist. Additionally, while they provide numerical examples to illustrate their points, they do not provide any real-world examples or case studies that could further demonstrate how their findings can be applied in practice. Finally, while they discuss both mono-link and multi-link networks, they focus more heavily on multi-link networks than mono-link ones; thus, readers may get an incomplete picture if they only read this article without researching other sources as well.