Slow dynamics and rare-region effects in the contact process on weighted tree networks.

@article{dor2012SlowDA,
  title={Slow dynamics and rare-region effects in the contact process on weighted tree networks.},
  author={G{\'e}za {\'O}dor and Romualdo Pastor-Satorras},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2012},
  volume={86 2 Pt 2},
  pages={
          026117
        }
}
  • G. Ódor, R. Pastor-Satorras
  • Published 1 June 2012
  • Materials Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We show that generic, slow dynamics can occur in the contact process on complex networks with a tree-like structure and a superimposed weight pattern, in the absence of additional (nontopological) sources of quenched disorder. The slow dynamics is induced by rare-region effects occurring on correlated subspaces of vertices connected by large weight edges and manifests in the form of a smeared phase transition. We conjecture that more sophisticated network motifs could be able to induce… 
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References

SHOWING 1-10 OF 136 REFERENCES
Rare-region effects in the contact process on networks.
TLDR
It is found that Griffiths phases can also emerge--even with constant epidemic rates--as a consequence of mere topological heterogeneity, and Griffithsphase phases are found in finite-dimensional networks as, for instance, a family of generalized small-world networks.
Griffiths phases on complex networks.
TLDR
It is found that Griffiths phases can also emerge in the absence of quenched disorder, as a consequence of topological heterogeneity in networks with finite topological dimension.
Langevin approach for the dynamics of the contact process on annealed scale-free networks.
TLDR
This work presents a detailed analysis of the contact process in terms of a Langevin equation, including explicitly the effects of stochastic fluctuations in the number of particles in finite networks, and examines the survival time for spreading experiments and the density of active sites in surviving runs.
Nonequilibrium phase transitions and finite-size scaling in weighted scale-free networks.
TLDR
This work considers nonequilibrium phase transitions in weighted scale-free networks, in which highly connected nodes have a relatively smaller ability to transfer infection, and solves the dynamical mean-field equations and discusses finite-size scaling theory.
Mean-field diffusive dynamics on weighted networks.
TLDR
A general formalism that allows to easily write down mean-field equations for any diffusive dynamics on weighted networks is introduced, and the concept of annealed weighted networks, in which such equations become exact is proposed.
Random walks on complex trees.
TLDR
It is observed that the absence of loops is reflected in physical observables showing large differences with respect to their looped counterparts, and the mean first passage time (MFPT) displays a logarithmic degree dependence, in contrast to the inverse degree shape exhibited in looped networks.
Non-mean-field behavior of the contact process on scale-free networks.
TLDR
An analysis of the classical contact process on scale-free networks shows an absorbing-state phase transition at a finite critical value of the control parameter, characterized by a set of exponents depending on the network structure.
Quasistationary simulations of the contact process on quenched networks.
TLDR
This work presents high-accuracy quasistationary simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs, and concludes that heterogeneous mean-field theory works for the Contact process on quenches networks, at odds with previous claims.
Evolution of networks
TLDR
The recent rapid progress in the statistical physics of evolving networks is reviewed, and how growing networks self-organize into scale-free structures is discussed, and the role of the mechanism of preferential linking is investigated.
Emergence of scaling in random networks
TLDR
A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
...
1
2
3
4
5
...