Stabilization of a structurally balanced complex network with similar nodes of different dimensions

Synchronization Mechanism for Controlled Complex Networks under Auxiliary Effect of Dynamic Edges

“…From the perspective of large-scale system theory, a complex network can be decomposed into two subsystems composed of nodes and edges, namely the node subsystem (NS) and the edge subsystem (ES). On this basis, an interconnected model of CDNs consisting of NSs and ESs is established [27][28][29][30][31][32]. The dynamic behaviors of the nodes and edges under the coupling relationship between the two subsystems have been studied.…”

“…Refs. [27][28][29] explored the dynamic characteristics of edges, which are rarely addressed, and the edge state tracking control problem was solved using an underactuated node control strategy. Ref.…”

“…Ref. [27] utilized heterogeneous controlled nodes to indirectly drive edge states and derived the correlation between the ES's state and network structure balance. In Ref.…”

“…[30,31], a control design method for achieving target tracking of nodes was discussed via the auxiliary role of the ES with and without edge-state observers. Although the modeling problem of dynamic edges and the mutual coupling dynamic behaviors between two subsystems have been investigated, the studies reported in [27][28][29][30][31][32] have shortcomings in terms of model universality and control design methods that urgently need to be resolved through further studies.…”

“…In Refs. [27][28][29]31,32], the edge models were in undirected or special vector form, and the controller design method was limited by pre-set coupling structures. In view of these gaps, this paper proposes a more general directed matrix model of dynamic edges based on related works.…”