Competing edge networks
We introduce a model for a pair of nonlinear evolving networks, defined over a common set of vertices, subject to edgewise competition. Each network may grow new edges spontaneously or through triad closure. Both networks inhibit the others growth and encourage the others demise. These nonlinear sto...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2012
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| _version_ | 1797051943639580672 |
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| author | Parsons, M Grindrod, P |
| author_facet | Parsons, M Grindrod, P |
| author_sort | Parsons, M |
| collection | OXFORD |
| description | We introduce a model for a pair of nonlinear evolving networks, defined over a common set of vertices, subject to edgewise competition. Each network may grow new edges spontaneously or through triad closure. Both networks inhibit the others growth and encourage the others demise. These nonlinear stochastic competition equations yield to a mean field analysis resulting in a nonlinear deterministic system. There may be multiple equilibria; and bifurcations of different types are shown to occur within a reduced parameter space. This situation models competitive communication networks such as BlackBerry Messenger displacing SMS; or instant messaging displacing emails. © 2012 Elsevier B.V. |
| first_indexed | 2024-03-06T18:26:18Z |
| format | Journal article |
| id | oxford-uuid:0814a660-2ee3-451e-98e6-1d7a22851df8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:26:18Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:0814a660-2ee3-451e-98e6-1d7a22851df82022-03-26T09:11:03ZCompeting edge networksJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0814a660-2ee3-451e-98e6-1d7a22851df8EnglishSymplectic Elements at Oxford2012Parsons, MGrindrod, PWe introduce a model for a pair of nonlinear evolving networks, defined over a common set of vertices, subject to edgewise competition. Each network may grow new edges spontaneously or through triad closure. Both networks inhibit the others growth and encourage the others demise. These nonlinear stochastic competition equations yield to a mean field analysis resulting in a nonlinear deterministic system. There may be multiple equilibria; and bifurcations of different types are shown to occur within a reduced parameter space. This situation models competitive communication networks such as BlackBerry Messenger displacing SMS; or instant messaging displacing emails. © 2012 Elsevier B.V. |
| spellingShingle | Parsons, M Grindrod, P Competing edge networks |
| title | Competing edge networks |
| title_full | Competing edge networks |
| title_fullStr | Competing edge networks |
| title_full_unstemmed | Competing edge networks |
| title_short | Competing edge networks |
| title_sort | competing edge networks |
| work_keys_str_mv | AT parsonsm competingedgenetworks AT grindrodp competingedgenetworks |