Time-dependent Pinning Control Of Complex Networks

With the rapid growth of the information technology,we have a deep understanding of human living environment and natural system.The human social production activities are tightly related to the complex networks and complex systems.Therefore,the complex networks and complex systems have become a hot topic in recent years.Synchronization is an important dynamic behavior in complex systems.It is essential for complex networks to study the synchronization.In order to achieve the advantages of synchronization,how to control the synchronization in complex networks has attracted much attention.Pinning control is a high efficient and low-cost control method for complex networks.In this thesis,we study the control synchronization in the time-varying complex networks.In the first part,we mainly study the time-varying pinning control in complex networks.We apply the time-varying control strength ?(t)to pinning the whole network.Based on the master stability function(MSF),we analyze the theory and simulate the numerical results.Compared with the constant pinning control,it is seen that the time-varying pinning control can enlarge the controllable synchronization region.Then,we apply the same control strategy to pinning partial nodes in the network.It is found that the network can be synchronized in the smaller critical control strength,and the controlled synchronization region can be enlarged.In the second part,we study the pinning control in multiple forms of time-varying complex networks.We apply the time-varying coupling strength and control strength to control the network.?(t)=?0(1.0 + sin(2?f?t))and ?(t)=?0(1.0 +sin(2?f?t))denote the coupling strength and the control strength,respectively.For global pinning control,we find that the critical control strength is reduced when the frequency of the coupling strength is the same as the frequency of the control strength,compared to the constant pinning control.When the frequency of the coupling strength is the same as the frequency of the control strength and the phase difference between them is ?,the critical control strength is larger,but the controlled synchronization region is obviously enlarged.Then,we apply the same control strategy to pinning partial nodes in the complex networks.Also,it is found that the critical control strength can be reduced,and the controlled synchronization region can be increased.The use of time-varying control methods to control the complex networks can reduce the control cost of achieving complete synchronization.And,it can also maintain the system in complete synchronization in a larger control strength region,achieving the better control effect than constant pinning control.