Study On Quasi-synchronization Of Stochastic Complex Networks With Impulsive Effect

Complex dynamic networks exist widely in the real world.With the rapid development of computer technology and network communication technology,the synchronization of complex dynamic networks has become a hot research topic in the information age,relevant research results are constantly emerging.However,the existing research mainly considers the complex network model with constant node parameters and single time delay effect.So far,the synchronization behavior of complex dynamic networks with heterogeneous node parameters and mixed timedelay effects has not been fully studied,and some problems have not been solved.Based on this,the synchronization control problem of the complex network model with heterogeneous perturbations and hybrid coupling time-delay is deeply analyzed and studied.The full text is divided into four chapters.The details are as follows:In Chapter 1,the research significance and development of complex dynamic networks,synchronization behavior and impulse control are introduced,this paper briefly introduces the research results of the synchronous control of complex dynamic networks with time delay and the synchronous control of complex dynamic networks with time delay and Markov-jumping coefficient in recent years,finally,the main contents of this thesis are pointed out.In Chapter 2,the synchronization of impulse control for complex dynamic networks with hybrid coupled delays and heterogeneous external disturbances is studied.The dynamic equations of the nodes take into account the heterogeneous and bounded external disturbances,and the coupling process of the network takes into account both the coupling delay and the mixed state delay.The model is more general.We use the state information to design the feedback controller in pulse form.By constructing a difference inequality with multiple mixed delays,combining Lyapunov function method and inequality technique,a sufficient criterion for global exponential quasi-synchronization of complex dynamic networks is established.The theoretical results obtained improve the existing literature,and can be verified by solving the linear matrix inequality,which is convenient for practical application.In Chapter 3,the synchronization control problem of complex dynamic networks with time-delay and heterogeneous perturbations and Markov-switch parameters is studied.The complex network model considered in this paper has Markov-switch parameters and hybrid coupling delays,and its nodes are affected by both external disturbance and random noise.The model has more complex structure and wide applicability.Based on the coupling state information,a impulsive controller is constructed and the synchronization error model is established.By constructing different Lyapunov functions,using mixed delay difference inequality technique,random analysis theory and matrix theory,the sufficient criterion of quasi-synchronism depending on switching mode is established,the results of the existing literature are improved.Finally,numerical examples and simulation are given to verify the validity and feasibility of the theoretical results.In Chapter 4,we summarize the main research contents and innovation,and point out some future research directions.