Studies On Complex Network Modeling And Dynamical Processes In Typical Networks

The last few years have witnessed tremendous activities devoted to the characterization and understanding of networked systems. Indeed many large complex networks arise in a vast number of natural and artificial systems. In this thesis, complex network modeling and dynamical processes in typical complex networks (i.e., random networks, small-world networks and scale-free networks) are studied by using statistics physics, operational research and computer simulation. This thesis focuses on investigating load distributions, traffic jamming, cascading failures and synchronization with discrete time and discrete state in typical complex networks. The main contents of this thesis are summarized as follows:(1) On the issue of complex network modeling, firstly, three typical complex network models, i.e., Erdos-Renyi random network model, Watts-Strogatz small-world network model and Barabasi-Albert scale-free network model are simply introduced. Then, an asymmetrical evolving network model and a weighted model evolution with traffic flow are presented. In the asymmetrical evolving network model, the concept of utility is introduced. The probability for the new node chosing old nodes to be connected is proportional to the utility of the old node. Moreover, the utilities of the connected nodes update asymmetrically. Both theoretical analysis and simulation results show that the distribution of utility follows a power law, and the degree distribution is between the exponential distribution and power law distribution,In the weighted model evolution with traffic flow, the state of traffic flow is considered as a node, an edge between two nodes is created if one state of traffic flow can evolve into another at one time step, and the transferred traffic volume is considered as the weight of the edge. Non-linear relationship between the strength and degree of the node is studied theoretically and by numerical tests.(2) Based on user equilibrium model, this thesis discusses load distribution in typical complex networks (especially in scale-free networks) under the effect of congestion. It is found that load distribution may follow as exponential distribution or power law distribution in scale-free networks. Based on cell transmission model, traffic jamming in gradient networks is analyzed. The difference of the jamming factor between random networks and scale-free networks is found to increase firstly, and then decrease and finally increase, with the increase of the degree of traffic jamming. In terms of the traffic evolving rule, which is similar to random walks under the condition of congestion, the diffusion of congestion and flow fluctuations in typical complex networks are studied. And two extended cases, i.e., stopping traffic flows and stopping and guiding traffic flows are presented to relieve local congestion. Simulation results show that the two extended cases can not aggravate global congestion, and the second extended case can be used to relieve global congestion and flow flunctions in scale-free networks (i.e., heterogeneous networks).(3) On the issue of cascading failures, a simple fiber bundle model is extended to scale-free networks to study the behavior of edge failures. Theoretical analysis and simulation results show that, when the exponent of the scaling between the load and degree of the node is larger than the exponent of the degree distribution, there is a scaling relationship between the average rate of failed links and the network size, where the exponent is-1, independent of the exponent of degree distribution. Based on user equilibrium model, the effects of congestion and network structure on cascading failures are investigated. Simulation results show that the effect of congestion has an active effect and the effect of network heterogeneity has a negative effect on influencing the behavior of cascading failures. In other words, the performance of the network against cascading failures can be improved by properly increasing the congestion of the network, and scale-free network with larger value of the exponent of degree distribution is more prone to suffer from cascading failures. Finally, a model for cascading failures fitting urban traffic networks is proposed, and the effect of feedback is also studied. We find that the effect of feedback can reduce the discrepancy between random networks and scale-free networks against cascading failures.(4) In this thesis, a synchronization model with both discrete time and discrete state is presented. A transfer matrix for the node's state is introduced to determine its self-driven function. Simulation results in typical complex networks show that, according to the synchronization index, the coupling strength is divided into four regions:the increasing region, the maximum region, the decreasing region and the oscillation region. It may shed new insights on investigating synchronization behavior in complex networks.