The Synchronization Performance Research Of Complex Heterogeneous Networks With Degree Correlations

Complex network is an abstract description of complex systems in the real world. Many real networks have the features of assortative or disassortative mixing pattern, such as social networks are assortative, while biological networks or technological systems are generally disassortative which is lacking in typical theoretical network models. It is well known that Watts-Strogatz small-world model, ER random model, and even Barabasi-Albert scale-free network all show non-correlation feature.In this paper, a mechanism for which models the emergence of the degree correlation property of complex networks is proposed. Degree distribution of the network model meets power-law distribution which meets the real world’s situation. Through adjusting a parameter in this novel model, this correlation-adjustable network model can exhibit fundamentally different degree correlation mixing patterns with a scale-free degree sequence. It is found that the degree distribution of the network model determines its degree correlation. The degree correlation coefficient of the novel model does not change with the scale of the network. The range of correlation coefficient r also shows certain rules with changes in the exponent. The stronger the heterogeneity of the degree distribution is, the smaller the range r is.For the correlation-adjustable network model, the structural properties of networks and its robust and fragile features are also investigated. It is found that a positive correlation network is more compact than negative one, which has a shorter average path length. The simulation of the clustering coefficient also meets the situation of the real world well. In the study of robust and fragile characteristics with random failures and deliberate attacks, no correlation network model in the face of deliberate attacks shows robust.To study the phase synchronization performance of correlation-adjustable network model, a phase synchronization criterion of Kuramoto model is proposed which theoretically proves Lyapunov stability of equilibrium points. The criterion is used in the analysis of the phase synchronization performance, which is analyzed from two respects:the same power law parameters, and different power law parameters. The results show that the larger network is easier to achieve synchronization, and there is a critical coupling strength which makes network synchronization performance saturated; positive correlation network, homogeneous network has better network synchronization performance.