Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer model
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1155/2015/354918 http://hdl.handle.net/11449/171824 |
Resumo: | We study a cancer model given by a three-dimensional system of ordinary differential equations, depending on eight parameters, which describe the interaction among healthy cells, tumour cells, and effector cells of immune system. The model was previously studied in the literature and was shown to have a chaotic attractor. In this paper we study how such a chaotic attractor is formed. More precisely, by varying one of the parameters, we prove that a supercritical Hopf bifurcation occurs, leading to the creation of a stable limit cycle. Then studying the continuation of this limit cycle we numerically found a cascade of period-doubling bifurcations which leads to the formation of the mentioned chaotic attractor. Moreover, analyzing the model dynamics from a biological point of view, we notice the possibility of both the tumour cells and the immune system cells to vanish and only the healthy cells survive, suggesting the possibility of cure, since the interactions with the immune system can eliminate tumour cells. |
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Repositório Institucional da UNESP |
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Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer modelWe study a cancer model given by a three-dimensional system of ordinary differential equations, depending on eight parameters, which describe the interaction among healthy cells, tumour cells, and effector cells of immune system. The model was previously studied in the literature and was shown to have a chaotic attractor. In this paper we study how such a chaotic attractor is formed. More precisely, by varying one of the parameters, we prove that a supercritical Hopf bifurcation occurs, leading to the creation of a stable limit cycle. Then studying the continuation of this limit cycle we numerically found a cascade of period-doubling bifurcations which leads to the formation of the mentioned chaotic attractor. Moreover, analyzing the model dynamics from a biological point of view, we notice the possibility of both the tumour cells and the immune system cells to vanish and only the healthy cells survive, suggesting the possibility of cure, since the interactions with the immune system can eliminate tumour cells.Departamento de Matemática e Computação, Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista (UNESP)Departamento de Matemática e Computação, Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista (UNESP)Universidade Estadual Paulista (Unesp)Galindo, Marluci Cristina [UNESP]Nespoli, Cristiane [UNESP]Messias, Marcelo [UNESP]2018-12-11T16:57:18Z2018-12-11T16:57:18Z2015-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://dx.doi.org/10.1155/2015/354918Abstract and Applied Analysis, v. 2015.1687-04091085-3375http://hdl.handle.net/11449/17182410.1155/2015/3549182-s2.0-849266568022-s2.0-84926656802.pdf375722566905631769482537989528810000-0002-0690-0857Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengAbstract and Applied Analysis0,3430,343info:eu-repo/semantics/openAccess2024-06-19T14:31:50Zoai:repositorio.unesp.br:11449/171824Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:30:39.660450Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer model |
title |
Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer model |
spellingShingle |
Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer model Galindo, Marluci Cristina [UNESP] |
title_short |
Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer model |
title_full |
Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer model |
title_fullStr |
Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer model |
title_full_unstemmed |
Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer model |
title_sort |
Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer model |
author |
Galindo, Marluci Cristina [UNESP] |
author_facet |
Galindo, Marluci Cristina [UNESP] Nespoli, Cristiane [UNESP] Messias, Marcelo [UNESP] |
author_role |
author |
author2 |
Nespoli, Cristiane [UNESP] Messias, Marcelo [UNESP] |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Galindo, Marluci Cristina [UNESP] Nespoli, Cristiane [UNESP] Messias, Marcelo [UNESP] |
description |
We study a cancer model given by a three-dimensional system of ordinary differential equations, depending on eight parameters, which describe the interaction among healthy cells, tumour cells, and effector cells of immune system. The model was previously studied in the literature and was shown to have a chaotic attractor. In this paper we study how such a chaotic attractor is formed. More precisely, by varying one of the parameters, we prove that a supercritical Hopf bifurcation occurs, leading to the creation of a stable limit cycle. Then studying the continuation of this limit cycle we numerically found a cascade of period-doubling bifurcations which leads to the formation of the mentioned chaotic attractor. Moreover, analyzing the model dynamics from a biological point of view, we notice the possibility of both the tumour cells and the immune system cells to vanish and only the healthy cells survive, suggesting the possibility of cure, since the interactions with the immune system can eliminate tumour cells. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-01-01 2018-12-11T16:57:18Z 2018-12-11T16:57:18Z |
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://dx.doi.org/10.1155/2015/354918 Abstract and Applied Analysis, v. 2015. 1687-0409 1085-3375 http://hdl.handle.net/11449/171824 10.1155/2015/354918 2-s2.0-84926656802 2-s2.0-84926656802.pdf 3757225669056317 6948253798952881 0000-0002-0690-0857 |
url |
http://dx.doi.org/10.1155/2015/354918 http://hdl.handle.net/11449/171824 |
identifier_str_mv |
Abstract and Applied Analysis, v. 2015. 1687-0409 1085-3375 10.1155/2015/354918 2-s2.0-84926656802 2-s2.0-84926656802.pdf 3757225669056317 6948253798952881 0000-0002-0690-0857 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Abstract and Applied Analysis 0,343 0,343 |
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.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128371029180416 |