On Stability And Synchronization Behaviors For Networks Systems

Recently,since complex dynamical networks can describe a variety of real sys-tems,such as ecosystems,internet,biological neural networks,social networks and biomolecular networks,science and engineering researchers from different areas are all have strong concern to it.The aim of this work is to investigate the stabili-ty and synchronization control of several complex dynamic network models,which include stability of neural networks via periodically impulsive control,finite-time synchronization of neural networks via feedback control,finite-time synchroniza-tion of neural networks via aperiodically intermittent control as well as complete synchronization of complex networks via aperiodically intermittent control.In the first chapter,the histories and developments of complex network and neu-ral network,stability and synchronization control are presented.And,the research content of this paper is introduced.In the second chapter,we concern the problem of exponential stability for a class of Cohen-Grossberg neural networks with impulse time window and time-varying delays.In the letter,the impulsive effects we considered can be stochastically occurred at a definitive time window and the impulsive controllers we considered can be nonlinear and even rely on the states of all the neurons.By utilizing Lyapunov functional theory,inequality technique and the analysis method,we obtain some exponential stability criteria for the Cohen-Grossberg neural networks.Finally,numerical simulations are given to show the effectiveness of the derived results.In the third chapter,we concern the problem of global and local finite-time synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying delays by designing an appropriate feedback controller.Through a nonlinear transformation,we derive an alternative system from the considered memristor-based Cohen-Grossberg neural networks.Then,by considering the finite-time synchronization of the alternative system,we obtain some finite-time synchro-nization criteria for the considered memristor-based Cohen-Grossberg neural net-works.These results generalize and extend some previous known works on conven-tional Cohen-Grossberg neural networks.Finally,numerical simulations are given to present the effectiveness of the theoretical results.In the forth chapter,we concern the exponential synchronization problem for hybrid-coupled delayed dynamical networks via pinning aperiodically intermittent control.Different from previous works,the delayed coupling term considered here contains the transmission delay and self-feedback delay,and the intermittent con-trol can be aperiodic.By establishing a new differential inequality and constructing Lyapunov function,several useful criteria are derived analytically to realise expo-nential synchronization for both free time delay(there is no restriction imposed on the delay and the control(and/or rest)width)and small time delay(the delay is smaller than the minimum of control width).Finally,a numerical example is given to demonstrate the validness of the proposed scheme.In the fifth chapter,we concern the exponential synchronization problem for hybrid-coupled delayed dynamical networks via aperiodically intermittent control.Different from previous works,the delayed coupling term considered here contains the transmission delay and self-feedback delay,and the intermittent control can be aperiodic.By utilizing mathematical induction and Lyapunov functions,several useful criteria are derived analytically to realise exponential synchronization for a class of coupled complex network.As a special case,some sufficient conditions ensuring the exponential synchronization for a class of coupled neural network are obtained.Finally,a numerical example is given to demonstrate the validness of the proposed scheme.In the sixth chapter,the problem of the finite-time synchronization(FTS)is studied for a class of delay neural networks(DNNs)via aperiodically intermittent control.Based on the finite-time stability theory,several new conditions ensuring FTS of two DNNs are derived by establishing a very useful differential inequality and constructing a new Lyapunov function.And,the upper bounds of the settling time for synchronization are estimated.Finally,numerical simulations show the effectiveness of the derived results and the developed method.In the seventh chapter,we summary the results of this study,point out the existing problems and prospect for future research.