Adaptive Control of the Structural Balance for a Class of Complex Dynamical Networks

In social networks,the structural balance is a state of a group of individuals(nodes)with established mutual relationships(connection relationships)between them.It is easy to see that a social network can be described by a complex dynamical network model composed of the nodes subsystem(NS)and the connection relationships subsystem(CS),where the two subsystems are usually coupled with each other.It implies that the dynamic changes of nodes'states may cause the structural balance in CS.However,few papers have discussed the relationship between the structural balance and the specific dynamic changes of the nodes'states.This paper proposes a model of complex dynamical networks,and mainly focuses on the dynamic changes of states in NS which can lead to the structural balance in CS.It is proved that if each state in NS is doing a specific dynamic motion via the controller with the parameter adaptive law,then the CS can track a given structural balance matrix via the effective coupling and the structural balance can be achieved.Such a result can be regarded as an explanation of the relationship between the structural balance and the specific dynamic changes of the nodes'states.Finally,the simulations verify the effectiveness of the proposed method.