Two-layer Coupled Synchronization Dynamics In Complex Networks

A complex network is a large-scale network with complex topology and dynamical behavior.Networks with some or all of the properties in self-organization,self-similarity,attractors,small worlds,and scale-free are generally referred to as complex networks.Many real-world networks interact with each other,such as airline networks and railroad networks,social relationship networks and disease propagation networks or power transmission networks and computer control networks,etc.The coupling between networks generates interesting dynamical phenomena,and synchronization as one of them plays a crucial role in the study of complex networks.The two-layer network model constructed in this paper consists of an information transmission layer and an opinion coordination layer,with nodes corresponding to each other in the two layers of the network.The lower information transmission layer is a random network,modeled as a biased random wandering process.The upper opinion coordination layer is generated by a scale-free network simulation and is modeled by the set of N Kuramoto oscillators.The motion bias of an information packet on a node in the information transmission layer is determined by the degree of the corresponding node in the upper network,and the natural frequency of the oscillator of a node in the opinion coordination layer is proportional to the effectiveness of the information of the corresponding node in the lower network,and the two layers of the network are coupled to each other to produce explosive synchronization.This model is more applicable to social networks,where the lower layer is the actual physical contact network,where people are known randomly and exchange information with each other,full of uncertainty;the upper layer is the virtual online network,where people communicate and interact with each other through different social platforms.In this paper,three cases of unweighted,Gaussian weighted and exponential weighted in undirected network are investigated.Changing the bias parameterαand the power exponentγ,the synchronization order parameter r varies between 0 and 1 with the coupling strengthλ.And the network will also move from asynchronous to synchronous state.Find the maximum critical coupling strengthλ_c and compare the synchronization performance of the three networks.For different bias parameterα,the values of r are all between 0.9 and1 and the network basically reaches the synchronized state in the unweighted and undirected network.The values of r all approaches 1 indefinitely and the network reaches the fully synchronized state in the Gaussian weighted and undirected network.In the exponential weighted and undirected network the values of r are all between 0.95 and 1 and the network basically reaches a full synchronization state.Comparing the three undirected networks,it is found that the unweighted network has the worst synchronization performance,the exponential weighted has the middle performance,and the Gaussian weighted network has the best performance.Therefore,increasing the weight can improve the synchronization ability of the network.The Gaussian weighted network has a small waveform range of the curves towards synchronization.The correspondingλ_cis the smallest and r_min is the largest.At the same time,it is also more consistent with the degree distribution of online social networks in the real world.In the following research,we will focus on establishing a more reasonable social network model and continue to explore the synchronization dynamic characteristics of intelligent networks in the intelligent era to better solve practical problems.