Critical behavior of the contact process on small-world networks

Ferreira, Ronan Silva; Ferreira, Silvio C.

doi:10.1140/epjb/e2013-40534-0

Cited by 32 publications

(39 citation statements)

References 31 publications

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“…We consider both homogeneous and heterogeneous networks. In random regular (RR) networks [39] all vertices have the same degree k i = k and connections are performed at random following the configuration model [40] avoiding both multiple and self connections. In the Erdös-Renyi (ER) model [8], each pair of vertices is connected with probability p. When the size of the graph N → ∞, its degree distribution is a Poissonian with a finite mean k = pN .…”

Section: Model and Networkmentioning

confidence: 99%

Dynamical correlations and pairwise theory for the symbiotic contact process on networks

2019

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The two-species symbiotic contact process (2SCP) is a stochastic process where each vertex of a graph may be vacant or host at most one individual of each species. Vertices with both species have a reduced death rate, representing a symbiotic interaction, while the dynamics evolves according to the standard (single species) contact process rules otherwise. We investigate the role of dynamical correlations on the 2SCP on homogeneous and heterogeneous networks using pairwise mean-field theory. This approach is compared with the ordinary one-site theory and stochastic simulations. We show that our approach significantly outperforms the one-site theory. In particular, the stationary state of the 2SCP model on random regular networks is very accurately reproduced by the pairwise mean-field, even for relatively small values of vertex degree, where expressive deviations of the standard mean-field are observed. The pairwise approach is also able to capture the transition points accurately for heterogeneous networks and provides rich phase diagrams with transitions not predicted by the one-site method. Our theoretical results are corroborated by extensive numerical simulations.

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Section: Model and Networkmentioning

confidence: 99%

Dynamical correlations and pairwise theory for the symbiotic contact process on networks

2019

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“…every time the system tries to visit an absorbing state it jumps to an active configuration previously visited during the simulation (a new initial condition). Details of the method with applications to dynamical processes on networks can be found elsewhere [15,33].…”

Section: Threshold For Arbitrary Random Networkmentioning

confidence: 99%

“…The puzzle behind this apparent paradox is that cluster approximations underestimate the real threshold, and the convergence is expected only in the limit of large cluster approximations. A homogeneous triplet approximation (HTA) for the CP on unclustered networks yields the threshold [33]:…”

Section: Threshold For Arbitrary Random Networkmentioning

confidence: 99%

Heterogeneous pair-approximation for the contact process on complex networks

Mata

Ferreira

2014

New J. Phys.

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Recent works have shown that the contact process running on the top of highly heterogeneous random networks is described by the heterogeneous mean-field theory. However, some important aspects such as the transition point and strong corrections to the finite-size scaling observed in simulations are not quantitatively reproduced in this theory. We develop a heterogeneous pair-approximation, the simplest mean-field approach that takes into account dynamical correlations, for the contact process. The transition points obtained in this theory are in very good agreement with simulations. The proximity with a simple homogeneous pair-approximation is elicited showing that the transition point in successive homogeneous cluster approximations moves away from the simulation results. We show that the critical exponents of the heterogeneous pairapproximation in the infinite-size limit are the same as those of the one-vertex theory. However, excellent matches with simulations, for a wide range of network sizes, are obtained when the sub-leading finite-size corrections given by the new theory are explicitly taken into account. The present approach can be suited to dynamical processes on networks in general providing a profitable strategy to analytically assess and fine-tune theoretical corrections.

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“…[23][24][25][26] and references therein). Having two processes in the game, we can distinguish three possible outcomes: any of the processes wins or we have a dynamical equilibrium between them.…”

Section: Discussionmentioning

confidence: 99%

Competing contact processes in the Watts-Strogatz network

2016

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Abstract. We investigate two competing contact processes on a set of Watts-Strogatz networks with the clustering coefficient tuned by rewiring. The base for network construction is one-dimensional chain of N sites, where each site i is directly linked to nodes labelled as i ± 1 and i ± 2. So initially, each node has the same degree ki = 4. The periodic boundary conditions are assumed as well. For each node i the links to sites i + 1 and i + 2 are rewired to two randomly selected nodes so far not-connected to node i. An increase of the rewiring probability q influences the nodes degree distribution and the network clusterization coefficient C. For given values of rewiring probability q the set N (q) = {N1, N2, . . . , NM } of M networks is generated. The network's nodes are decorated with spin-like variables si ∈ {S, D}. During simulation each S node having a D-site in its neighbourhood converts this neighbour from D to S state. Conversely, a node in D state having at least one neighbour also in state D-state converts all nearest-neighbours of this pair into D-state. The latter is realized with probability p. We plot the dependence of the nodes S final density n .

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Critical behavior of the contact process on small-world networks

Cited by 32 publications

References 31 publications

Dynamical correlations and pairwise theory for the symbiotic contact process on networks

Dynamical correlations and pairwise theory for the symbiotic contact process on networks

Heterogeneous pair-approximation for the contact process on complex networks

Competing contact processes in the Watts-Strogatz network

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