Modelling Accelerating Growth with IntermittentProcesses in Evolving Networks

In this paper, the acceleratingly growing network model withintermittent processes is proposed. In the growing network, thereexist both accelerating and intermittent processes. The network isgrown from the number of nodes m₀ and the number of links added with each new node is a nonlinearly increasing functionm+aN^β(t)f(t), where N(t) is the number of nodes present attime t. f(t) is the periodic and bistable function withperiod T, whose values are 1 and 0 indicating acceleratingand intermittent processes, respectively. Here we denote the ratioτ of acceleration time to whole one. We study the degree distribution p(k) of the model, focusing on the dependence of p(k) on the network parameters τ, T, m, a, N, andβ. It is found that there exists a phase transition pointk_c such that if k<k_c, then p(k) obeys a power-law distribution with exponent -γ₁, while if k>k_c, thenp(k) exhibits a power-law distribution with exponent -γ₂.Moreover, the exponents γ₁ and γ₂ are independent of τ, T, m, a, and N, while they depend only on theparameter β. More interesting, the phase transition point isdescribed by k_c=aN^β, which is equal to the value at whichp(k) is maximum in GM model.