Condensation Phenomena In Non-equilibrium Complex Networks

Critical behaviors play an important role in the evolution of the complex networks. It is well known that fitness model can be mapped into Bose statistics in a suitable way and a condensation phase, similar to Bose-Einstein statistics occurs. Condensation phenomena are also appeared in the growing network with super-linear preferential attachment, if the super-linear parameter ? ? 1. In present papers we combine the connection mechanism of both complex networks and define a"chemical potential"? formally, we hope to give a unified description to both networks. After theoretical analysis and numerical simulations we draw a conclusion: Though the condensation phenomena are similar in both networks, they are different phases since they stem from different connection mechanisms.The application of Tsallis statistics into complex networks is another point of this paper. Since the complex systems with properties of self-organized criticality, fractal structures and power laws are a natural arena of Tsallis statistics, it is a valuable application of Tsallis statistics into complex networks. We introduce the q -form of Tsallis statistics into the dynamics of complex network evolution, where q is a dimensionless parameter and get the result of Tsallis mapping, the simulation results tell us that when q≠1 the critical temperature T_c~q moved compare with the critical temperature TB E of standard statistics. And our results come back to standard statistics in the case of q→1.