Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.2/2124 |
Resumo: | In a recent paper, Laurencot and van Roessel (2010 J. Phys. A: Math. Theor., 43, 455210) studied the scaling behaviour of solutions to a two-species coagulation–annihilation system with total annihilation and equal strength coagulation, and identified cases where self-similar behaviour occurs, and others where it does not. In this paper, we proceed with the study of this kind of system by assuming that the coagulation rates of the two different species need not be equal. By applying Laplace transform techniques, the problem is transformed into a two-dimensional ordinary differential system that can be transformed into a Lotka–Volterra competition model. The long-time behaviour of solutions to this Lotka–Volterra system helps explain the different cases of existence and nonexistence of similarity behaviour, as well as why, in some cases, the behaviour is nonuniversal, in the sense of being dependent on initial conditions. |
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Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systemsEquações de coagulação-aniquilaçãoSoluções autosemelhantesEquações de Lotka-VolterraIn a recent paper, Laurencot and van Roessel (2010 J. Phys. A: Math. Theor., 43, 455210) studied the scaling behaviour of solutions to a two-species coagulation–annihilation system with total annihilation and equal strength coagulation, and identified cases where self-similar behaviour occurs, and others where it does not. In this paper, we proceed with the study of this kind of system by assuming that the coagulation rates of the two different species need not be equal. By applying Laplace transform techniques, the problem is transformed into a two-dimensional ordinary differential system that can be transformed into a Lotka–Volterra competition model. The long-time behaviour of solutions to this Lotka–Volterra system helps explain the different cases of existence and nonexistence of similarity behaviour, as well as why, in some cases, the behaviour is nonuniversal, in the sense of being dependent on initial conditions.FPC, JTP e RS foram parcialmente financiados pelo CAMGSD-LARSyS através do financiamento plurianual atribuido pela Fundação para a Ciência e Tecnologia (Portugal)Institute of PhysicsRepositório AbertoCosta, Fernando Pestana daPinto, João TeixeiraSasportes, RafaelRoessel, Henry J. van2012-06-25T16:49:21Z2012-062012-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/2124engCosta, Fernando Pestana da [et al.] - Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems. "Journal of Physics A [Em linha]: Mathematical and Theoretical". ISSN 1751-8113 (Print) 1751-8121 (Online). Vol. 45 (2012), p. 1-161751-8113 (Print)info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-16T15:15:31Zoai:repositorioaberto.uab.pt:10400.2/2124Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:43:43.330893Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems |
title |
Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems |
spellingShingle |
Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems Costa, Fernando Pestana da Equações de coagulação-aniquilação Soluções autosemelhantes Equações de Lotka-Volterra |
title_short |
Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems |
title_full |
Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems |
title_fullStr |
Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems |
title_full_unstemmed |
Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems |
title_sort |
Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems |
author |
Costa, Fernando Pestana da |
author_facet |
Costa, Fernando Pestana da Pinto, João Teixeira Sasportes, Rafael Roessel, Henry J. van |
author_role |
author |
author2 |
Pinto, João Teixeira Sasportes, Rafael Roessel, Henry J. van |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
Costa, Fernando Pestana da Pinto, João Teixeira Sasportes, Rafael Roessel, Henry J. van |
dc.subject.por.fl_str_mv |
Equações de coagulação-aniquilação Soluções autosemelhantes Equações de Lotka-Volterra |
topic |
Equações de coagulação-aniquilação Soluções autosemelhantes Equações de Lotka-Volterra |
description |
In a recent paper, Laurencot and van Roessel (2010 J. Phys. A: Math. Theor., 43, 455210) studied the scaling behaviour of solutions to a two-species coagulation–annihilation system with total annihilation and equal strength coagulation, and identified cases where self-similar behaviour occurs, and others where it does not. In this paper, we proceed with the study of this kind of system by assuming that the coagulation rates of the two different species need not be equal. By applying Laplace transform techniques, the problem is transformed into a two-dimensional ordinary differential system that can be transformed into a Lotka–Volterra competition model. The long-time behaviour of solutions to this Lotka–Volterra system helps explain the different cases of existence and nonexistence of similarity behaviour, as well as why, in some cases, the behaviour is nonuniversal, in the sense of being dependent on initial conditions. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-06-25T16:49:21Z 2012-06 2012-06-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.2/2124 |
url |
http://hdl.handle.net/10400.2/2124 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Costa, Fernando Pestana da [et al.] - Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systems. "Journal of Physics A [Em linha]: Mathematical and Theoretical". ISSN 1751-8113 (Print) 1751-8121 (Online). Vol. 45 (2012), p. 1-16 1751-8113 (Print) |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Institute of Physics |
publisher.none.fl_str_mv |
Institute of Physics |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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