The Research On Evolving Models With Logistic Growth

The complex systems and their evolutionary development in the real world make the connection between people closer and deeper.Using the complex network models contained in these systems to explain various complex phenomena and behaviors in reality is the common goal of scientists in many fields such as mathematics,physics,biology,and engineering.It is of great theoretical significance to explore the evolving rules of complex network models to solve the deep problems in the actual network structure,to find the evolving rules more close to the real life,to control and optimize the evolving development characteristics of the networks.Since many evolving rules in the real society have the characteristics of rapid growth first,then slow growth after reaching a certain level,they present a typical phenomenon of retard growth.The paper first introduces the development and research directions of complex networks,the basic topological properties of networks,and the practical significance of complex network research in real life.Then,based on the characteristics of Logistic retard growth,two types of evolving network models are proposed in this paper,which are local Logistic model and global Logistic model.The evolution of the degree of a single node in the two types of models is obtained through the average field theory.Numerical simulations are used to verify that the local Logistic network has a bilateral power-law degree distribution.Combined with the numerical simulation method,the topological characteristics of the the average path length,global efficiency,clustering coefficient and assortativity coefficient are studied under the conditions of different maximum capacity,growth rate and initial value.For the global Logistic network,the number of edges added to the network at each step meets the bel1 distribution,and the clustering coefficient is significantly greater than that of the BA scale-free network and the local Logistic network.It is feasible to adjust the number of edges added to the global Logistic network at each step to obtain a network model with variable clustering coefficients.Finally,through the Laplacian matrices of the local Logistic network models and global Logistic network models,the internal factors that affect the synchronization are obtained.