Study On Dynamic Behaviors And Control For Several Kinds Of Complex Network Systems

Complex system is one of the key objects of complexity science and system science in the 21st century,many phenomena in nature and human society can be described and characterized by complex systems.As one of the main manifestations of complex systems,complex network has been attracted considerable attention by many scholars recently since it can help people to understand and study complex system more better Based on the theory of complex system,this paper studies the dynamic behaviors and control for several kinds of complex network systems by integrating the related technolo-gies and methods of differential equation theory,neural network and modern control theory.On the one hand,the synchronization issues between complex networks under different control strategies are studied,including the finite-time synchronization under intermittent control,finite-time and fixed-time synchronization under feedback control and adaptive control as well as the H? exponential synchronization under sampled-data based event-triggered control.On the other hand,based on the theoretical research of complex network,the dynamic behavior of rumor propagation is modeled,analyzed and controled in complex networks.The specific studies of this paper are as followsIn the first part,both the finite-time and fixed-time synchronization of delayed complex networks are considered.Firstly,a lemma is improved to deal with the finite-time synchronization problem under intermittent control.Then,based on the estab-lished stability theory and some important inequalities,some criteria are given in view of the intermittent control to ensure the synchronization between systems in a finite time.Secondly,under the same one feedback control strategy and by adjusting the key control parameters,the criteria on finite-time and fixed-time synchronization are established respectively.It is found that the setting time estimation of the finite-time synchronization depends not only on the initial value but also on the time delay,while the setting time estimation of fixed-time synchronization has nothing to do with these two factors.Finally,a detailed numerical analysis is presented to verify the correctness of the corresponding results.In the second part,the synchronization of Cohen-Grossberg neural networks with time delays and discontinuous activation functions is analyzed.Based on the theories of differential inclusions,measurable selection and finite-time stability,the synchronization between systems is respectively considered under the feedback control and adaptive control in the sense of Filippov solution.Through adjusting a key control parameter,exponential synchronization,finite-time synchronization and fixed-time synchronization can be realized respectively,and the corresponding setting time is estimated.To verify the correctness of the conclusions,a numerical example is present,ed.In the third part,the finite-time and fixed-time synchronization of coupled mem-ristive neural networks are concerned.Firstly,a lemma is generalized to illustrate the relationship between finite-time and fixed-time stabilities.Secondly,Under the assumptions that are weaker than Lipschitz,the synchronization between systems is respectively discussed under feedback control and adaptive control by the proposed lemma,and the synchronization criteria of finite-time and fixed-time are established respectively in the sense of 1-norm and 2-norm.It is found that the setting time of fixed-time synchronization estimated in the sense of 1-norm is more accurate than that in the sense of 2-norm.Finally,to illustrate the effectiveness of control strategies,a detailed numerical analysis is given.In the fourth part,through designing an aperiodic sampled-data based event-triggered scheme,the H? exponential synchronization control problem for complex networks with quantized control input is studied.Firstly,based on the principle of event-triggered control,two different feedback controllers are designed.Then,utilizing the theories of discrete-time Lyapunov and sampling system,the exponential synchro-nization of the system is investigated in the absence of disturbance input is studied,and the criteria based on matrix inequality is established.Secondly,due to the non-negligibility of the disturbance input,the H? performance of the system is discussed in the presence of disturbance input.Finally,the validity of the control strategies and the correctness of the theoretical results are verified by numerical simulation.In the last part,the rumor propagation model with heterogeneous network struc-ture in multi-lingual environment is studied.Firstly,considering the influence of ed-ucational factors on spreaders,a new rumor propagation model is established.Then,combining the stability theory of differential equation and Lyapunov method,the local and global stabilities of the equilibrium point are analyzed.Secondly,through the sen-sitivity analysis for the model parameters,it is found that the education mechanism has a significant impact on rumor propagation.Therefore,in view of the thought of optimal control,a control strategy of optimizing the education mechanism is proposed.Final-ly,the corresponding numerical analysis is provided to demonstrate the correctness of obtained results and the effectiveness of control strategy.