Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response
The dynamics of the model for tumor-immune system competition with negative immune response and with one delay investigated. We show that the asymptotic behavior depends crucially on the time delay parameter. We are particularly interested in the study of the Hopf bifurcation problem to predict the...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/95296 |
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| _version_ | 1832559428664033280 |
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| author | Radouane Yafia |
| author_facet | Radouane Yafia |
| author_sort | Radouane Yafia |
| collection | DOAJ |
| description | The dynamics of the model for tumor-immune system competition with
negative immune response and with one delay investigated. We show that the asymptotic behavior depends
crucially on the time delay parameter. We are particularly
interested in the study of the Hopf bifurcation problem to predict
the occurrence of a limit cycle bifurcating from the nontrivial
steady state, by using the delay as a parameter of bifurcation.
The obtained results provide the oscillations given by the
numerical study in M. Gałach (2003), which are observed in
reality by Kirschner and Panetta (1998). |
| format | Article |
| id | doaj-art-8b17894dc4524d77a37debdd85f9fb6d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8b17894dc4524d77a37debdd85f9fb6d2025-02-03T01:30:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/9529695296Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune responseRadouane Yafia0Département de Mathématiques et Informatique, Faculté des Sciences, Université Chouaib Doukkali, BP 20, El Jadida 2400, MoroccoThe dynamics of the model for tumor-immune system competition with negative immune response and with one delay investigated. We show that the asymptotic behavior depends crucially on the time delay parameter. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the nontrivial steady state, by using the delay as a parameter of bifurcation. The obtained results provide the oscillations given by the numerical study in M. Gałach (2003), which are observed in reality by Kirschner and Panetta (1998).http://dx.doi.org/10.1155/DDNS/2006/95296 |
| spellingShingle | Radouane Yafia Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response Discrete Dynamics in Nature and Society |
| title | Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response |
| title_full | Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response |
| title_fullStr | Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response |
| title_full_unstemmed | Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response |
| title_short | Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response |
| title_sort | hopf bifurcation in a delayed model for tumor immune system competition with negative immune response |
| url | http://dx.doi.org/10.1155/DDNS/2006/95296 |
| work_keys_str_mv | AT radouaneyafia hopfbifurcationinadelayedmodelfortumorimmunesystemcompetitionwithnegativeimmuneresponse |