| The research on the structure and dynamics of multi-layer networks is a frontier topic in the field of network science research.In multi-layer networks,the connection between single-layer networks directly affects the propagation,diffusion and synchronization of the entire multi-layer network.At present,for the research on the general structure of multi-layer networks,there is no systematic theory or method yet.People can only start with some simple multi-layer network structures to explore how their different inter-layer connection methods affect the overall dynamic behavior of the multilayer network.In this thesis,the above problem is explored through graph theory and numerical calculations,we attempt to find more optimized connection between layers of the network,which is a two-layer network with a chain structure in each single layer and there are two edges between the layers.First of all,according to the master stability function method,this thesis proves that when the synchronous region is unbounded,multi-layer networks with the same network structure at all layers have a certain interlayer coupling strength threshold under any one-to-one inter-layer connection mode,and the threshold value maximizes the synchronizability of the entire network,which is the synchronizability of its single-layer network.Secondly,the simulations in this thesis preliminarily show that when there are only two edges between layers,the optimal inter-layer connection positions of the two-layer chain network is when the two links are respectively located at 1/4 and 3/4 of each chain,while the worst connection positions are respectively one end of the chain and its neighbor node.Subsequently,we discuss in detail about the optimal connection mode of two-layer chain networks respectively when the number of single-layer nodes is 4N,4N + 1,4N + 2,and 4N + 3.We find that: Except for the case where the single-layer nodes number is 4N,in which there are 3 optimal connection modes;the optimal connection mode in the cases of the other three single-layer nodes numbers are all unique.Finally,we propose the expression of the optimal inter-layer coupling strength of the two-layer chain networks,then by calculating the optimal inter-layer coupling strength values of the network under different cases of single-layer nodes’ number,we verify the correctness of the expression. |
