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Slow dynamics of the contact process on complex networks
The Contact Process has been studied on complex networks exhibiting different
kinds of quenched disorder. Numerical evidence is found for Griffiths phases and other
rare region effects, in ErdËťos RĂ©nyi networks, leading rather generically to anomalously
slow (algebraic, logarithmic,...) relaxation. More surprisingly, it turns out that Griffiths
phases can also emerge in the absence of quenched disorder, as a consequence of sole
topological heterogeneity in networks with finite topological dimension. In case of scalefree
networks, exhibiting infinite topological dimension, slow dynamics can be observed
on tree-like structures and a superimposed weight pattern. In the infinite size limit the
correlated subspaces of vertices seem to cause a smeared phase transition. These results
have a broad spectrum of implications for propagation phenomena and other dynamical
process on networks and are relevant for the analysis of both models and empirical data