Adaptive Pinning Synchronization of Complex Networks with Negative Weights and Its Application in Traffic Road Network

As local traffic congestion and uncertainty factors existing on roads may lead to cascading failures or even large area traffic network congestion, a pinning control method is proposed to divert the traffic and then restore the smooth flow of traffic. To eliminate the impacts of uncertainties and negative weights for the traffic network performance, the adaptive pinning control and coupling adjustment strategies are designed to estimate controller parameters and adjust coupling strength to compensate for the impacts on the pinned nodes and unpinned nodes. Based on Lyapunov stability theory, adaptive pinning controllers and network adjusters are developed to guarantee the achievement of network synchronization even in the presence of the uncertainties and negative weights. In addition, we investigate the effects of the type of nodes on pinning synchronization performance. Numerical simulations show that if the network’s degree and the single node energy index are considered, better synchronization performance can be obtained by comparing with the pervious pinning schemes.