Finite-time Cluster Synchronization And Resource Control Of Infectious Diseases For The Complex Networks

In the past ten years,finite-time synchronization of the complex networks has attracted great attention of scholars in many fields,because of its interdisciplinary characteristics of aerospace,communication,cryptography and efficient synchronization efficiency.The synchronization efficiency refers to the two important factors of synchronization time and synchronization speed when the finite-time synchronization problem of the system is being studied.At present,finite-time synchronization is still one of the important and popular research topics in the research of the complex network synchronization.In addition,with the deepening of research into the diffusion,transmission and control of information as well as viruses,single or single-link networks fail to meet the actual needs.Therefore,the multi-layer network formed by the interaction between layers of multiple subnetworks began to arouse the interest of many scholars.Nowadays,the research of propagation dynamics on multi-layer networks has become one of the most cutting-edge topics in the field of the complex networks.Firstly,based on the previous research on finite-time identical synchronization,this thesis discusses finite-time cluster synchronization of the system by introducing the phenomenon of synchronization impulses,desynchronization impulses and time delay that may appear in the real system.Afterwards,the star structure is introduced on the basis of multi-layer network topology,to discuss the control of diseases in multi-layer star coupling network.To be specific,the research contents of this thesis are as follows:1.Finite-time cluster synchronization for the delayed complex dynamical network with synchronizing or desynchronizing impulses is studied.Based on impulsive control theory,Lyapunov stability theory,matrix inequality,graph theory as well as the other related theoretical knowledge,together with the classification of nodes and the setting of impulse sequences,two controllers with synchronization impulses or desynchronization impulses are designed.As a result,some sufficient conditions and the upper bound of the time for finite-time cluster synchronization can be derived when the delayed network system with synchronizing or desynchronizing impulses reaches the synchronization state.Finally,the correctness of the theoretical result is verified by MATLAB software.2.The problem of infectious disease resource control in two-layer star coupling networks is studied.In the first place,the multi-layer star-coupling network topology is combined with the classic SIS model of infectious diseases.Second of all,a set of infection probability values are assumed according to the propagation characteristics of the intra-layer central nodes,the intra-layer leaf nodes,the inter-layer central nodes and the inter-layer leaf nodes,the infection probability between the leaf nodes,the center nodes and the resource quantity are obtained.Furthermore,a set of discrete dynamic propagation equations is constructed.Finally,the relationship between the infection quantity of each layer network and the resource quantity,the infection probability between the inter-layer central nodes and the resource quantity,the inter-layer leaf nodes and the resource quantity are acquired.Finally,the correctness of the theoretical result is verified by MATLAB.