Synchronization, Control and Robustness of Higher-Order Complex Networks

Description

Complex networks research has seen very rapid developments in the past two decades, with fruitful results contributing to network science and its applications, and is fast evolving to a more advanced level of studies today. Typical subjects in complex dynamical networks research carried out by systems engineers include network control, network synchronization and network robustness studies.The PI of this proposal is one of the few pioneers in the aforementioned focal research subjects of the field. More precisely, the PI and colleagues developed the very first network synchronization criterion and they were the first to characterize the optimal structures of complex networks with the best possible synchronizability; the PI and colleagues were among the earliest to study complex network pinning controllability and obtained necessary and sufficient conditions for MIMO network controllability, which also suggest an schematic approach to the design of MIMO pinning controllers; the PI and colleagues were pioneers in investigating complex network robustness of controllability against malicious attacks by means of destructive node- and/or edge-removal, to evaluate the network robustness and suggest resilience methods.Success notwithstanding, the above research accomplishments were achieved for conventional complex networks using classical graph-theoretic tools. The present proposal takes a further step forward to advance the current research to a higher level on higher-order complex networks, which requires more powerful tools from algebraic topology theory and methods involving higher-order simplexes, using measures and techniques based on Euler characteristic indexes and Petti numbers, among others.Specifically, this project has three objectives:Objective 1: Developing higher-order network synchronization criterion and methodsObjective 2: Developing higher-order network pinning controllability criterion and methodsObjective 3: Investigating structural and controllability robustness of higher-order networksBased on the PI’s well-developed analytic techniques and computational methods, this project has a solid basis and is promising, which will significantly contribute to the fields of network science and engineering upon its completion.