Slow dynamics of the contact process on complex networks
arXiv:1302.0808 · doi:10.1051/epjconf/20134404005
Abstract
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 Erd\H os Rényi 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 scale-free 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.
8 pages, 3 figs, conference proceedings of ICNP1 Oran, Algeria 2012, to appear in EPJ Web of Conferences
References in corpus (29)
- Statistical mechanics of complex networks
- Critical phenomena in complex networks
- Universality classes in nonequilibrium lattice systems
- Generation of uncorrelated random scale-free networks
- Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
- Geographical dispersal of mobile communication networks
- Rare region effects at classical, quantum, and non-equilibrium phase transitions
- Localization and Spreading of Diseases in Complex Networks
- Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
- Designing optimal transport networks
- Griffiths phases on complex networks
- Non mean-field behavior of the contact process on scale-free networks
- Griffiths Singularities in the Disordered Phase of a Quantum Ising Spin Glass
- Langevin approach for the dynamics of the contact process on annealed scale-free networks
- Localization, anomalous diffusion and slow relaxations: a random distance matrix approach
- Temporal Griffiths Phases
- Non-equilibrium Phase Transitions with Long-Range Interactions
- Renormalization group study of random quantum magnets
- Routes to thermodynamic limit on scale-free networks
- Nonequilibrium phase transitions and finite size scaling in weighted scale-free networks
- Anomalous lifetime distributions and topological traps in ordering dynamics
- Rare region effects in the contact process on networks
- Robust short-term memory without synaptic learning
- Enhancement of Tc in the Superconductor-Insulator Phase Transition on Scale-Free Networks
- Slow dynamics and rare-region effects in the contact process on weighted tree networks
- Random elastic networks : strong disorder renormalization approach
- Superdiffusion in a class of networks with marginal long-range connections
- Scaling behavior of the contact process in networks with long-range connections
- Competition between quenched disorder and long-range connections: A numerical study of diffusion