Condensation Of Particles And Epidemic Spreading On Complex Network

The study of complex networks has obtained an increasing interest in recent years. Its key point is how the network topology influences the dynamical behaviors on it. Two of the most important dynamic processes on complex networks are the particle condensation and epidemic spreading, whose studies will provide us some insight to the dynamics on complex networks. This thesis will study the dynamical behaviors on complex networks by three aspects, i.e., the influence of periodic switching of nodes on epidemic spreading, the influence of the change of network structure on particle condensation and epidemic spreading, and the influence of clustering coefficient on particle condensation and epidemic spreading.We first study how the periodic switching of nodes affects the epidemic spreading. We choose the SIS model of epidemic spreading. By considering the zero range process (ZRP), we study the epidemic spreading on complex networks. The previous results show that when the nodes in the network are partially occupied, the final infected number is determined by the hopping rates of the particles. Moreover, there is an optimal value of the hopping rate in which the infected number will be the largest. We discover that when the periodic switching is considered, the infected number will change with the hopping rates of particles. When the switching period is fixed, the infected number will increase slowly at first with the increase of the hopping rate and then increase fast when the rate reaches an appropriate value. Our numerical simulations show that the final infected number will exhibit periodic oscillation when the nodes of network are periodic switching.Next, we study how the condensation of particles and epidemic spreading are affected by network topology. The nodes are considered to be potential wells with its depth being equivalent to the degree of the node. We let the hopping rate of particle be the function of both potential depth and the temperature. We have studied three typical network structures, i.e., the random network, scale-free network and a third in between them. We find that there is an optimal temperature T. for all the three networks and the condensation occurs nearby Tc. When condensation happens, the infected number will reach the largest, and the number of infected number in the scale-free networks is larger than other two cases.Finally, we consider how the cluster coefficient influences the condensation of particles and epidemic spreading. The dependence of hopping rate on the potential depth and temperature is kept. We find that for different cluster coefficients, there is always a condensation nearby Tc where the infected number will be the largest. However, we are interesting to find that with the increase of clustering coefficient, both the number of condensed particles and the infected number will decrease.In sum, our results show that the dynamical behaviors on complex networks will be seriously influenced by the elements of network topology, the status of the nodes (open or close), and the clustering coefficient.