A Yule-Simon process with memoryC. Cattuto1, 2, V. Loreto2 and V. D. P. Servedio3, 1
1 Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi Compendio Viminale, 00184 Roma, Italy
2 Dipartimento di Fisica, Università "La Sapienza" - P.le A. Moro 2 00185 Roma, Italy
3 Dipartimento di Informatica e Sistemistica, Università "La Sapienza" Via Salaria 113, 00198 Roma, Italy
received 5 July 2006; accepted 29 August 2006
published online 20 September 2006
The Yule-Simon model has been used as a tool to describe the growth of diverse systems, acquiring a paradigmatic character in many fields of research. Here we study a modified Yule-Simon model that takes into account the full history of the system by means of a hyperbolic memory kernel. We show how the memory kernel changes the properties of preferential attachment and provide an approximate analytical solution for the frequency distribution density as well as for the frequency-rank distribution.
05.10.-a - Computational methods in statistical physics and nonlinear dynamics.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
89.20.Ff - Computer science and technology.
© EDP Sciences 2006