We demonstrate a comprehensive framework that accounts for citation dynamics of scientific papers and for the age distribution of references. We show that citation dynamics of scientific papers is nonlinear and this nonlinearity has far-reaching cons
equences, such as diverging citation distributions and runaway papers. We propose a nonlinear stochastic dynamic model of citation dynamics based on link copying/redirection mechanism. The model is fully calibrated by empirical data and does not contain free parameters. This model can be a basis for quantitative probabilistic prediction of citation dynamics of individual papers and of the journal impact factor.
We discuss microscopic mechanisms of complex network growth, with the special emphasis of how these mechanisms can be evaluated from the measurements on real networks. As an example we consider the network of citations to scientific papers. Contrary
to common belief that its growth is determined by the linear preferential attachment, our microscopic measurements show that it is driven by the nonlinear autocatalytic growth. This invalidates the scale-free hypothesis for the citation network. The nonlinearity is responsible for a dramatic dynamical phase transition: while the citation lifetime of majority of papers is 6-10 years, the highly-cited papers have practically infinite lifetime.
We perform experimental verification of the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose citation network of Physics papers and traced citation history of 4
0,195 papers published in one year. Contrary to common belief, we found that citation dynamics of the individual papers follows the emph{superlinear} preferential attachment, with the exponent $alpha= 1.25-1.3$. Moreover, we showed that the citation process cannot be described as a memoryless Markov chain since there is substantial correlation between the present and recent citation rates of a paper. Basing on our findings we constructed a stochastic growth model of the citation network, performed numerical simulations based on this model and achieved an excellent agreement with the measured citation distributions.
