Condensation of Self-Driven Particles in Scale-Free Networks

A new simple model of self-driven particles in scale-free networks is introduced to understand the emergence of condensation in the natural world. In the model, at each time step, particles are driven to choose their next habitats according to the particle numbers at both the present habitats and neighbors. It is found that the hub effect results in the condensation. The present numerical results as well as the theoretical analysis of condensation transition show the criterion of condensation. Both simulations and theoretical analysis display that there are three phases for different hopping probabilities δ: non-condensation (δ<δ_c), partial condensation (δ_c≤ δ<1), and complete condensation (δ≥δ_c'= 1), and the mean occupation particle number at the stationary state is also obtained. Moreover, the noise effect on self-driven particles is studied, and it makes particle numbers at nodes tend towards being identical.