An economical model with Allee effect
Autor(a) principal: | |
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Data de Publicação: | 2009 |
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/10400.13/3776 |
Resumo: | We formulate a mathematical model based on Marx theory of economics. The profit rate r is considered as a function of both the exploitation rate e and the organic composition of the capital k. This model possesses a new property, commonly used in biology, called the Allee effect, in which the profit rate declines to zero if it falls below a certain threshold. It is represented by the difference equation rnþ1 ¼ fa(rn), which is a family of unimodal maps depending on the parameter a, where a measures the relative growth of the exploitation rate when the profit rate is zero. Moreover, the model predicts a period-doubling bifurcation scenario as the parameter a increases. Finally, we allow the parameter a fluctuate periodically which leads to a periodic non-autonomous difference equations. |
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An economical model with Allee effectProfit rateOrganic composition of the capitalExploitation rateAllee effectNon-autonomous periodic systemsBust and boom in the profit rate.Faculdade de Ciências Exatas e da EngenhariaWe formulate a mathematical model based on Marx theory of economics. The profit rate r is considered as a function of both the exploitation rate e and the organic composition of the capital k. This model possesses a new property, commonly used in biology, called the Allee effect, in which the profit rate declines to zero if it falls below a certain threshold. It is represented by the difference equation rnþ1 ¼ fa(rn), which is a family of unimodal maps depending on the parameter a, where a measures the relative growth of the exploitation rate when the profit rate is zero. Moreover, the model predicts a period-doubling bifurcation scenario as the parameter a increases. Finally, we allow the parameter a fluctuate periodically which leads to a periodic non-autonomous difference equations.Taylor and FrancisDigitUMaLuís, RafaelElaydi, SaberOliveira, Henrique2021-10-27T08:56:18Z2009-01-01T00:00:00Z2009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.13/3776engLuís, R., Elaydi, S., & Oliveira, H. (2009). An economical model with Allee effect. Journal of Difference Equations and Applications, 15(8-9), 877-894. https://doi.org/10.1080/1023619080246892010.1080/10236190802468920info: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:RCAAP2022-09-05T12:56:50Zoai:digituma.uma.pt:10400.13/3776Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T15:07:10.314787Repositório 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 |
An economical model with Allee effect |
title |
An economical model with Allee effect |
spellingShingle |
An economical model with Allee effect Luís, Rafael Profit rate Organic composition of the capital Exploitation rate Allee effect Non-autonomous periodic systems Bust and boom in the profit rate . Faculdade de Ciências Exatas e da Engenharia |
title_short |
An economical model with Allee effect |
title_full |
An economical model with Allee effect |
title_fullStr |
An economical model with Allee effect |
title_full_unstemmed |
An economical model with Allee effect |
title_sort |
An economical model with Allee effect |
author |
Luís, Rafael |
author_facet |
Luís, Rafael Elaydi, Saber Oliveira, Henrique |
author_role |
author |
author2 |
Elaydi, Saber Oliveira, Henrique |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
DigitUMa |
dc.contributor.author.fl_str_mv |
Luís, Rafael Elaydi, Saber Oliveira, Henrique |
dc.subject.por.fl_str_mv |
Profit rate Organic composition of the capital Exploitation rate Allee effect Non-autonomous periodic systems Bust and boom in the profit rate . Faculdade de Ciências Exatas e da Engenharia |
topic |
Profit rate Organic composition of the capital Exploitation rate Allee effect Non-autonomous periodic systems Bust and boom in the profit rate . Faculdade de Ciências Exatas e da Engenharia |
description |
We formulate a mathematical model based on Marx theory of economics. The profit rate r is considered as a function of both the exploitation rate e and the organic composition of the capital k. This model possesses a new property, commonly used in biology, called the Allee effect, in which the profit rate declines to zero if it falls below a certain threshold. It is represented by the difference equation rnþ1 ¼ fa(rn), which is a family of unimodal maps depending on the parameter a, where a measures the relative growth of the exploitation rate when the profit rate is zero. Moreover, the model predicts a period-doubling bifurcation scenario as the parameter a increases. Finally, we allow the parameter a fluctuate periodically which leads to a periodic non-autonomous difference equations. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-01-01T00:00:00Z 2009-01-01T00:00:00Z 2021-10-27T08:56:18Z |
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/10400.13/3776 |
url |
http://hdl.handle.net/10400.13/3776 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Luís, R., Elaydi, S., & Oliveira, H. (2009). An economical model with Allee effect. Journal of Difference Equations and Applications, 15(8-9), 877-894. https://doi.org/10.1080/10236190802468920 10.1080/10236190802468920 |
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 |
Taylor and Francis |
publisher.none.fl_str_mv |
Taylor and Francis |
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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799129941793570816 |