Research On Quasi-Synchronization Of Two Classes Of Heterogeneous Complex Networks With Parameter Mismatches

Complex networks consist of massive nodes and the edges connecting nodes exist widely in the real world,such as the Internet,mobile communication networks,neural networks,metabolic networks,WWW,social networks,and so on.The synchronization and control problems of complex networks have attracted much attention from researchers in different disciplines due to its theoretical challenges and wide application,which is a hot pot in the study of science.In the existing literature,most of the research objects of network synchronization are identical networks.But in practical life,complex networks are often the heterogeneous networks composed of nonidentical nodes.The parameter mismatches among systems is one of the reasons causing the heterogeneous networks.Because there is a nonzero error bound between the state of the nodes and the target state in the heterogeneous network with parameter mismatches,we call this synchronization state is quasi-synchronization.Quasi-synchronization provides a new way to investigate the synchronization of heterogeneous networks.Quasi-synchronization problem of the two classes of heterogeneous networks with parameter mismatches was mainly considered in the paper.It mainly includes the following two aspects:Firstly,the quasi-synchronization problem of a heterogeneous network coupled by Duffing oscillators in the presence of parameter mismatches is studied.Different from the most of the existing research methods,this paper does not consider adding any external controller,only depending on the internal coupling between the nodes of the network,and changing the coupling strength to speed up the coupled heterogeneous Duffing oscillator network to reach quasi-synchronization.By selecting a reasonable Lyapunov function and through rigorous mathematical proof,some sufficient conditions for guaranteeing the heterogeneous Duffing oscillator coupled complex networks to achieve quasi-synchronization are obtained.Finally,the numerical examples are used to verify the validity of the theoretical results.Then,the quasi-synchronization of heterogeneous Lur'e network with parameter mismatches is discussed through the aperiodically intermittent pinning control strategy.The quasi-synchronization of the heterogeneous Lur'e network with linearly time-delay coupled and nonlinearly time-delay coupled are considered separately.By designing the controller related to the node error,only some nodes in the network are controlled during a part of the time,and an appropriate Lyapunov function is constructed.Some criteria are obtained to guarantee the two types of heterogeneous Lur'e networks to achieve quasi-synchronization through the stability and related mathematical theory.In addition,several sufficient conditions to reach synchronization of the different types of the networks are also derived,such as linearly non-time-delay coupled and nonlinearly delay coupled simultaneously exist in the Lur'e networks,linearly time-delay coupled with parameter matches,and so on.The correctness of the theoretical results under the two conditions of linearly time-delay coupled and nonlinearly time-delay coupled are verified by using corresponding network systems consisted of six nodes whose dynamical behavior is Chua's circuit.