Synchronization in Scale Free networks with degree correlation

C. E. La Rocca, L. A. Braunstein, 2 and P. A. Macri Instituto de Investigaciones F́ısicas de Mar del Plata (IFIMAR)-Departamento de F́ısica, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata-CONICET, Funes 3350, (7600) Mar del Plata, Argentina. Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA Abstract In this paper we study a model of synchronization process on scale free networks with degreedegree correlations. This model was already studied on this kind of networks without correlations by Pastore y Piontti et al., Phys. Rev. E 76, 046117 (2007). Here, we study the effects of the degree-degree correlation on the behavior of the load fluctuations Ws in the steady state. We found that for assortative networks there exist a specific correlation where the system is optimal synchronized. In addition, we found that close to this optimally value the fluctuations does not depend on the system size and therefore the system becomes fully scalable. This result could be very important for some technological applications. On the other hand, far from the optimal correlation, Ws scales logarithmically with the system size.