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- Géza Odor
- Physical review. E, Statistical, nonlinear, and…
- 2003

The phase transition of the one-dimensional diffusive pair contact process is investigated by N cluster mean-field approximations and high precision simulations. The N=3,4 cluster approximations exhibit smooth transition line to absorbing state by varying the diffusion rate D with beta(2)=2 mean-field order parameter exponent of the pair density. This… (More)

- Miguel A Muñoz, Róbert Juhász, Claudio Castellano, Géza Odor
- Physical review letters
- 2010

Quenched disorder is known to play a relevant role in dynamical processes and phase transitions. Its effects on the dynamics of complex networks have hardly been studied. Aimed at filling this gap, we analyze the contact process, i.e., the simplest propagation model, with quenched disorder on complex networks. We find Griffiths phases and other rare-region… (More)

- Géza Odor
- Physical review. E, Statistical, nonlinear, and…
- 2003

Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n=3,4 parents, whereas explicit diffusion of single particles (A) is present are investigated in low dimensions by the mean-field approximation and simulations. The mean-field approximation of general nA-->(n+k)A, mA-->(m-l)A type of… (More)

- G Odor
- Physical review. E, Statistical, nonlinear, and…
- 2001

Recently an exact solution has been found by M. Henkel and H. Hinrichsen [J. Phys. A 34, 1561 (2001)] for the one-dimensional coagulation-production process: 2A-->A, AØA-->3A with equal diffusion and coagulation rates. This model evolves into the inactive phase independently of the production rate with t(-1/2) density decay law. This paper shows that… (More)

We show that efficient simulations of the Kardar-Parisi-Zhang interface growth in 2 + 1 dimensions and of the 3-dimensional Kinetic Monte Carlo of thermally activated diffusion can be realized both on GPUs and modern CPUs. In this article we present results of different implementations on GPUs using CUDA and OpenCL and also on CPUs using OpenCL and MPI. We… (More)

- T Antal, M Droz, A Lipowski, G Odor
- Physical review. E, Statistical, nonlinear, and…
- 2001

The critical properties of a simple prey-predator model are revisited. For some values of the control parameters, the model exhibits a line of directed percolationlike transitions to a single absorbing state. For other values of the control parameters one finds a second line of continuous transitions toward an infinite number of absorbing states, and the… (More)

- Géza Ódor
- Physical review. E, Statistical, nonlinear, and…
- 2013

I extend a previous work to susceptible-infected-susceptible (SIS) models on weighted Barabási-Albert scale-free networks. Numerical evidence is provided that phases with slow, power-law dynamics emerge as the consequence of quenched disorder and tree topologies studied previously with the contact process. I compare simulation results with spectral analysis… (More)

- Géza Odor, Romualdo Pastor-Satorras
- Physical review. E, Statistical, nonlinear, and…
- 2012

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… (More)

- Géza Odor
- Physical review. E, Statistical, nonlinear, and…
- 2013

The susceptible-infected-susceptible (SIS) model is one of the simplest memoryless systems for describing information or epidemic spreading phenomena with competing creation and spontaneous annihilation reactions. The effect of quenched disorder on the dynamical behavior has recently been compared to quenched mean-field (QMF) approximations in scale-free… (More)

- Róbert Juhász, Géza Ódor, Claudio Castellano, Miguel A Muñoz
- Physical review. E, Statistical, nonlinear, and…
- 2012

Networks and dynamical processes occurring on them have become a paradigmatic representation of complex systems. Studying the role of quenched disorder, both intrinsic to nodes and topological, is a key challenge. With this in mind, here we analyze the contact process (i.e., the simplest model for propagation phenomena) with node-dependent infection rates… (More)