Globally synchronized oscillations in complex cyclic games
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/104582 |
Resumo: | The rock-paper-scissors game and its generalizations with S > 3 species are well-studied models for cyclically interacting populations. Four is, however, the minimum number of species that, by allowing other interactions beyond the single, cyclic loop, breaks both the full intransitivity of the food graph and the one-predator, one-prey symmetry. Lütz et al. [J. Theor. Biol. 317, 286 (2013)] have shown the existence, on a square lattice, of two distinct phases, with either four or three coexisting species. In both phases, each agent is eventually replaced by one of its predators, but these strategy oscillations remain localized as long as the interactions are short ranged. Distant regions may be either out of phase or cycling through different food-web subloops (if any). Here we show that upon replacing a minimum fraction Q of the short-range interactions by long-range ones, there is a Hopf bifurcation, and global oscillations become stable. Surprisingly, to build such long-distance, global synchronization, the four-species coexistence phase requires fewer long-range interactions than the three-species phase, while one would naively expect the opposite to be true. Moreover, deviations from highly homogeneous conditions (χ = 0 or 1) increase Qc, and the more heterogeneous is the food web, the harder the synchronization is. By further increasing Q, while the three-species phase remains stable, the four-species one has a transition to an absorbing, single-species state. The existence of a phase with global oscillations for S > 3, when the interaction graph has multiple subloops and several possible local cycles, leads to the conjecture that global oscillations are a general characteristic, even for large, realistic food webs. |
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Rulquin, Charlotte Rose GiseleArenzon, Jeferson Jacob2014-10-15T02:12:50Z20141539-3755http://hdl.handle.net/10183/104582000922699The rock-paper-scissors game and its generalizations with S > 3 species are well-studied models for cyclically interacting populations. Four is, however, the minimum number of species that, by allowing other interactions beyond the single, cyclic loop, breaks both the full intransitivity of the food graph and the one-predator, one-prey symmetry. Lütz et al. [J. Theor. Biol. 317, 286 (2013)] have shown the existence, on a square lattice, of two distinct phases, with either four or three coexisting species. In both phases, each agent is eventually replaced by one of its predators, but these strategy oscillations remain localized as long as the interactions are short ranged. Distant regions may be either out of phase or cycling through different food-web subloops (if any). Here we show that upon replacing a minimum fraction Q of the short-range interactions by long-range ones, there is a Hopf bifurcation, and global oscillations become stable. Surprisingly, to build such long-distance, global synchronization, the four-species coexistence phase requires fewer long-range interactions than the three-species phase, while one would naively expect the opposite to be true. Moreover, deviations from highly homogeneous conditions (χ = 0 or 1) increase Qc, and the more heterogeneous is the food web, the harder the synchronization is. By further increasing Q, while the three-species phase remains stable, the four-species one has a transition to an absorbing, single-species state. The existence of a phase with global oscillations for S > 3, when the interaction graph has multiple subloops and several possible local cycles, leads to the conjecture that global oscillations are a general characteristic, even for large, realistic food webs.application/pdfengPhysical review. E, Statistical, nonlinear, and soft matter physics. Vol. 89, no. 3 (Mar. 2014), 032133, 6 p.BifurcaçãoTeoria dos jogosOscilacoesSincronizacaoGlobally synchronized oscillations in complex cyclic gamesEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000922699.pdf000922699.pdfTexto completo (inglês)application/pdf272944http://www.lume.ufrgs.br/bitstream/10183/104582/1/000922699.pdfd017392e2d75ec7ee7c353ea70b68278MD51TEXT000922699.pdf.txt000922699.pdf.txtExtracted Texttext/plain32052http://www.lume.ufrgs.br/bitstream/10183/104582/2/000922699.pdf.txt14b678b85bb707014137027da8b8a783MD52THUMBNAIL000922699.pdf.jpg000922699.pdf.jpgGenerated Thumbnailimage/jpeg2112http://www.lume.ufrgs.br/bitstream/10183/104582/3/000922699.pdf.jpg074d07b79d4ac7c9593aa62d9624d979MD5310183/1045822024-03-28 06:24:18.918014oai:www.lume.ufrgs.br:10183/104582Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2024-03-28T09:24:18Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Globally synchronized oscillations in complex cyclic games |
title |
Globally synchronized oscillations in complex cyclic games |
spellingShingle |
Globally synchronized oscillations in complex cyclic games Rulquin, Charlotte Rose Gisele Bifurcação Teoria dos jogos Oscilacoes Sincronizacao |
title_short |
Globally synchronized oscillations in complex cyclic games |
title_full |
Globally synchronized oscillations in complex cyclic games |
title_fullStr |
Globally synchronized oscillations in complex cyclic games |
title_full_unstemmed |
Globally synchronized oscillations in complex cyclic games |
title_sort |
Globally synchronized oscillations in complex cyclic games |
author |
Rulquin, Charlotte Rose Gisele |
author_facet |
Rulquin, Charlotte Rose Gisele Arenzon, Jeferson Jacob |
author_role |
author |
author2 |
Arenzon, Jeferson Jacob |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Rulquin, Charlotte Rose Gisele Arenzon, Jeferson Jacob |
dc.subject.por.fl_str_mv |
Bifurcação Teoria dos jogos Oscilacoes Sincronizacao |
topic |
Bifurcação Teoria dos jogos Oscilacoes Sincronizacao |
description |
The rock-paper-scissors game and its generalizations with S > 3 species are well-studied models for cyclically interacting populations. Four is, however, the minimum number of species that, by allowing other interactions beyond the single, cyclic loop, breaks both the full intransitivity of the food graph and the one-predator, one-prey symmetry. Lütz et al. [J. Theor. Biol. 317, 286 (2013)] have shown the existence, on a square lattice, of two distinct phases, with either four or three coexisting species. In both phases, each agent is eventually replaced by one of its predators, but these strategy oscillations remain localized as long as the interactions are short ranged. Distant regions may be either out of phase or cycling through different food-web subloops (if any). Here we show that upon replacing a minimum fraction Q of the short-range interactions by long-range ones, there is a Hopf bifurcation, and global oscillations become stable. Surprisingly, to build such long-distance, global synchronization, the four-species coexistence phase requires fewer long-range interactions than the three-species phase, while one would naively expect the opposite to be true. Moreover, deviations from highly homogeneous conditions (χ = 0 or 1) increase Qc, and the more heterogeneous is the food web, the harder the synchronization is. By further increasing Q, while the three-species phase remains stable, the four-species one has a transition to an absorbing, single-species state. The existence of a phase with global oscillations for S > 3, when the interaction graph has multiple subloops and several possible local cycles, leads to the conjecture that global oscillations are a general characteristic, even for large, realistic food webs. |
publishDate |
2014 |
dc.date.accessioned.fl_str_mv |
2014-10-15T02:12:50Z |
dc.date.issued.fl_str_mv |
2014 |
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Estrangeiro info:eu-repo/semantics/article |
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000922699 |
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eng |
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dc.relation.ispartof.pt_BR.fl_str_mv |
Physical review. E, Statistical, nonlinear, and soft matter physics. Vol. 89, no. 3 (Mar. 2014), 032133, 6 p. |
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