Binary-state dynamics on complex networks: Stochastic pair approximation and beyond
Theoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of nonlinear deterministic equations is assumed to characterize its dynamical and stationary properties. We develop in this work the stochastic formalism of the different...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.043370 |
| _version_ | 1797211142576144384 |
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| author | A. F. Peralta R. Toral |
| author_facet | A. F. Peralta R. Toral |
| author_sort | A. F. Peralta |
| collection | DOAJ |
| description | Theoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of nonlinear deterministic equations is assumed to characterize its dynamical and stationary properties. We develop in this work the stochastic formalism of the different compartmental approaches, these are the approximate master equation (AME), pair approximation (PA), and heterogeneous mean-field (HMF), in descending order of accuracy. The stochastic formalism allows us to enlarge the range of validity and applicability of compartmental approaches. This includes (i) the possibility of studying the role of the size of the system in the different phenomena reproduced by the models together with a network structure, (ii) obtaining the finite-size scaling functions and critical exponents of the macroscopic quantities, and (iii) the extension of the rate description to a more general class of models. |
| first_indexed | 2024-04-24T10:21:47Z |
| format | Article |
| id | doaj.art-8dc1afa4b5444b819fd5ac017828b28d |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:21:47Z |
| publishDate | 2020-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-8dc1afa4b5444b819fd5ac017828b28d2024-04-12T17:05:14ZengAmerican Physical SocietyPhysical Review Research2643-15642020-12-012404337010.1103/PhysRevResearch.2.043370Binary-state dynamics on complex networks: Stochastic pair approximation and beyondA. F. PeraltaR. ToralTheoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of nonlinear deterministic equations is assumed to characterize its dynamical and stationary properties. We develop in this work the stochastic formalism of the different compartmental approaches, these are the approximate master equation (AME), pair approximation (PA), and heterogeneous mean-field (HMF), in descending order of accuracy. The stochastic formalism allows us to enlarge the range of validity and applicability of compartmental approaches. This includes (i) the possibility of studying the role of the size of the system in the different phenomena reproduced by the models together with a network structure, (ii) obtaining the finite-size scaling functions and critical exponents of the macroscopic quantities, and (iii) the extension of the rate description to a more general class of models.http://doi.org/10.1103/PhysRevResearch.2.043370 |
| spellingShingle | A. F. Peralta R. Toral Binary-state dynamics on complex networks: Stochastic pair approximation and beyond Physical Review Research |
| title | Binary-state dynamics on complex networks: Stochastic pair approximation and beyond |
| title_full | Binary-state dynamics on complex networks: Stochastic pair approximation and beyond |
| title_fullStr | Binary-state dynamics on complex networks: Stochastic pair approximation and beyond |
| title_full_unstemmed | Binary-state dynamics on complex networks: Stochastic pair approximation and beyond |
| title_short | Binary-state dynamics on complex networks: Stochastic pair approximation and beyond |
| title_sort | binary state dynamics on complex networks stochastic pair approximation and beyond |
| url | http://doi.org/10.1103/PhysRevResearch.2.043370 |
| work_keys_str_mv | AT afperalta binarystatedynamicsoncomplexnetworksstochasticpairapproximationandbeyond AT rtoral binarystatedynamicsoncomplexnetworksstochasticpairapproximationandbeyond |