Synchronization Of Nonlinear Networks With Several Kinds Of Special Time Delay

Synchronization problem is one of the hotspots in nonlinear network research.Synchronization mainly investigates the coordination and consistency among individuals and individuals,individuals and groups,groups and groups.With the social networking process makes the network topology more and more complicated,the network scale becomes larger,increasing the difficulty of network control.Therefore,it is of great practical and theoretical significance to realize the synchronization of large-scale networks with appropriate control methods.With the development of synchronization research,the fields involved in synchronization are no longer limited to real value nonlinear networks.The synchronization of complex-valued nonlinear networks has become a new hotspot.The complex-value networks exist widely in real life.Compared with real-valued neural networks,the complex-valued neural networks have many unique characteristics.The complex-valued network is more efficient in solving certain scientific problems.Therefore,it is very important to investigate the synchronization of complex-valued networks.In the past,researchers constructed multiple complex-valued nonlinear network models according to satisfy the actual needs.Such as,complex chaotic system model,complex-valued neural network model,etc.A lot of research has been done on this kind of complex-valued nonlinear networks.On the other hand,Time delay exists widely in nonlinear networks.Time delay affects the stability of the network.Time delay is a non-negligible factor.Therefore,it is of practical significance to consider several kinds of special time delays in the synchronization study of nonlinear network systems.Based on the above discussion,in this paper,some basic concepts of complex networks and complex-valued neural networks are introduced.The complex network model with double time delay is constructed.The proper controller is designed to realize pinning control of large-scale complex network.Then the exponential module-phase synchronization of complex valued neural networks with time-varying delays is investigated.The results of mathematical proof and numerical simulation show that the method is effective and feasible.The main work of this paper is summarized as follows:1.Pinning synchronization of independent chaotic systems in complex networks with double time delays is studied.In this paper,the complex network model with node delay and coupling delay is constructed to solve the problem that different signals act on the same node in the complex network.And considering the cost of global control is too high,an adaptive pinning controller is designed to control some nodes in the network.In addition,theoretical proof and numerical simulation are adopted to show that the synchronization of the complex network with node delay and coupling delay can be realized by controlling some nodes in the network.It is indicated that the control strategy is effective and reliable.2.The problem of exponential module-phase synchronization of complex-valued neural networks with time-varying delay and stochastic perturbations is investigated.The time-delay of information transmission between nodes of neural network is not constant.According to this characteristic and considering the influence of external stochastic perturbations,we construct the complex-valued neural network model with time-varying delay and stochastic perturbations.And an adaptive control strategy is designed to achieve exponential mode-phase synchronization of complex-valued neural networks with time-varying delays.The sufficient condition for realizing synchronization is given by the Lyapunov stability theory.The reliability of theoretical analysis is verified by numerical simulation.Further,the real part and the imaginary part of complex value system are separated to achieve synchronization of the two neural networks respectively.The mode-phase synchronization only achieves the synchronization of mode state and phase state of the complex-valued network.Therefore,the synchronization condition is weakened.