Synchronization of Scale-Free Networks
Xin Jin, Zunshui Cheng · 2023
Chaos control and its applications have become one of the cutting-edge hot topics in nonlinear science. Compared with chaotic systems, hyperchaotic systems have more complex dynamic behaviors, and the randomness and uncertainty of the system have greatly increased. In this article, we will study the synchronization problem of linearly coupled hyperchaotic scale-free dynamic networks. For scale-free networks, the initial number of nodes, the number of newly added nodes, and the total number of network nodes will greatly affect the synchronization performance of the network. Using coupling method, Lyapunov function theorem and numerical simulation, we establish a BA scale-free network model, in which the state equation of the network nodes is described by a four-dimensional hyperchen chaotic system. By changing the number of new nodes added to the network$m$and the initial number of nodes$m_{0}$and the total number of nodes$N$, we observed the impact on the spectral radius of the Laplacian matrix, and further determined the synchronization state of the BA Complex network system. The obtained results indicate that increasing the number of new nodes in a chaotic network model can improve the synchronization of a given model. Finally, numerical simulations demonstrate the effectiveness of the obtained results.