Successive lag synchronization on dynamical networks: A perspective

¹ School of Computer and Information Security, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology - 541004, Guilin, China
² School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology - 541004, Guilin, China
³ Center for Applied Mathematics of Guangxi (GUET) - 541004, Guilin, China

Received: 3 January 2025
Accepted: 15 April 2025

Abstract

Synchronization plays a crucial role in complex dynamical networks, ensuring coordinated behaviors among interconnected nodes. Successive lag synchronization (SLS) is a distinctive synchronization type characterized by sequential synchronization between adjacent nodes with a fixed time delay. SLS specifically addresses scenarios with precisely structured and ordered interactions, presenting potential applications such as drone formations during military parades, autonomous vehicle platooning, and sequential industrial processes. Despite its theoretical and practical significance, systematic exploration of SLS remains limited, primarily due to challenges in ensuring stability across diverse dynamical networks and handling complex time delay disturbances. This Perspective provides a brief review of SLS, clearly defining its unique features, systematically analyzing stability considerations and implementation methods across various dynamical networks using both continuous and discontinuous controllers. Additionally, specific algorithms and control-free strategies for achieving SLS are discussed. Finally, this Perspective highlights key open issues and suggests promising future research directions.