Heterogeneous pair-approximation for the contact process on complex networks
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/16/5/053006 |
| _version_ | 1797751473338056704 |
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| author | Angélica S Mata Ronan S Ferreira Silvio C Ferreira |
| author_facet | Angélica S Mata Ronan S Ferreira Silvio C Ferreira |
| author_sort | Angélica S Mata |
| collection | DOAJ |
| description | 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 pair-approximation 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. |
| first_indexed | 2024-03-12T16:49:04Z |
| format | Article |
| id | doaj.art-e1a4b38d263b4810aacae1515a25a13d |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:49:04Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-e1a4b38d263b4810aacae1515a25a13d2023-08-08T11:26:41ZengIOP PublishingNew Journal of Physics1367-26302014-01-0116505300610.1088/1367-2630/16/5/053006Heterogeneous pair-approximation for the contact process on complex networksAngélica S Mata0Ronan S Ferreira1Silvio C Ferreira2Departamento de Física, Universidade Federal de Viçosa , 36570-000, Viçosa, MG, BrazilDepartment of Physics & I3N, University of Aveiro , 3810-193 Aveiro, PortugalDepartamento de Física, Universidade Federal de Viçosa , 36570-000, Viçosa, MG, BrazilRecent 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 pair-approximation 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.https://doi.org/10.1088/1367-2630/16/5/053006complex networkscritical phenomenamean-field theory89.75.Hc05.70.Jk05.10.Gg |
| spellingShingle | Angélica S Mata Ronan S Ferreira Silvio C Ferreira Heterogeneous pair-approximation for the contact process on complex networks New Journal of Physics complex networks critical phenomena mean-field theory 89.75.Hc 05.70.Jk 05.10.Gg |
| title | Heterogeneous pair-approximation for the contact process on complex networks |
| title_full | Heterogeneous pair-approximation for the contact process on complex networks |
| title_fullStr | Heterogeneous pair-approximation for the contact process on complex networks |
| title_full_unstemmed | Heterogeneous pair-approximation for the contact process on complex networks |
| title_short | Heterogeneous pair-approximation for the contact process on complex networks |
| title_sort | heterogeneous pair approximation for the contact process on complex networks |
| topic | complex networks critical phenomena mean-field theory 89.75.Hc 05.70.Jk 05.10.Gg |
| url | https://doi.org/10.1088/1367-2630/16/5/053006 |
| work_keys_str_mv | AT angelicasmata heterogeneouspairapproximationforthecontactprocessoncomplexnetworks AT ronansferreira heterogeneouspairapproximationforthecontactprocessoncomplexnetworks AT silviocferreira heterogeneouspairapproximationforthecontactprocessoncomplexnetworks |