Abstract
There are many behaviors with spatio-temporal characteristics in nature. Complex spatio-temporal networks (CSNs)-based on partial differential equations are to process such issues. This paper studies two synchronization boundary control methods. An adaptive boundary controller is first studied to ensure synchronization of the CSNs. Furthermore, a pinning adaptive boundary controller is proposed to achieve synchronization of the CSNs. Two sufficient criteria of synchronization and pinning synchronization are respectively obtained. Finally, two numerical examples demonstrate the effectiveness of the proposed theoretical results.