Complex dynamical networks have emerged as powerful tools for studying the characteristics and evolutions of various real-world social and engineering networks, such as multi-agent systems, power grids, biological networks, and epidemic spreading. The study of complex dynamical networks is crucial for understanding complex systems and provides a solid theoretical foundation for network science and engineering. Currently, scholars from different fields are especially interested in the issues of propagation and control in complex dynamical networks, leading to important achievements in related research areas.
The field of complex network propagation dynamics focuses on investigating the processes and patterns of information, diseases, and ideas spreading within complex network structures. Researchers employ various methods, including mathematical modeling, computational simulations, and analysis of real-world data, to explore the impact of network topology, node characteristics, and propagation rules on information dissemination. This research aims to reveal the patterns and characteristics of information propagation within complex networks, which has practical implications for understanding disease transmission mechanisms, social media information dissemination, and the influence of public opinions.
From the control discipline perspective, the study of complex dynamical networks mainly concentrates on synchronization and control, state estimation, topology identification, and propagation dynamics. Accurate network control is essential for promptly detecting network faults, ensuring normal network operation, and efficiently allocating network resources. Extensive research has been conducted in the field of complex network control, utilizing diverse control strategies, such as pulse control, pulse check control, hybrid control, adaptive control, sliding mode control, and model predictive control. Complex network control has been successfully applied in various domains, including formation control, attitude control, cooperative decision making, power networks, fault diagnosis, and clustering in data mining.
As network scales continue to expand, they become susceptible to external unreliable factors, such as topological changes, random noise, and data packet loss. These uncertain factors can significantly impact the stability of the entire complex network system, consequently affecting the effectiveness of network propagation analysis and control. Therefore, current research results in this field still have certain limitations, and there remain several meaningful and challenging questions that require further investigation. It is hoped that more experts and scholars will contribute to this field of research, sharing significant findings, and introducing new methods for the propagation and control of complex networks, ultimately applying them widely in practical engineering applications.
