Network Synchronization via Pinning Control from an Attacker-Defender Game Perspective

Abstract

The pinning control of complex networks is a hot topic of research in network science. However, most studies on pinning control ignore the impact of external interference on actual control strategies. To more comprehensively evaluate network synchronizability via pinning control in the attack–defense confrontation scenario, the paper constructs an attacker-defender game model. In the model, the attacker needs to control nodes in the network as much as possible. The defender will do their best to interfere with the attacker’s control of the network. Through a series of experiments, we find that the random attack strategy is always the dominant strategy of the attacker in various equilibriums. On the other hand, the defender needs to constantly change dominant strategy in equilibrium according to the set of defense strategies and cost constraints. In addition, scale-free networks with different network metrics can also influence the payoff matrix of the game. In particular, the average degree of the network has an obvious impact on the attacker’s payoff. Moreover, we further verify the correctness of the proposed attacker-defender game through a simulation based on the specific network synchronization dynamics. Finally, we conduct a sensitivity analysis in different network structures, such as the WS small-world network, the ER random network, and the Google network, to comprehensively evaluate the performance of the model.