Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response
This paper is devoted to the study of the stability of limit cycles of a system of nonlinear delay differential equations with a discrete delay. The system arises from a model of population dynamics describing the competition between tumor and immune system with negative immune response. We study th...
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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/2006/58463 |
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| _version_ | 1850213572024467456 |
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| author | Radouane Yafia |
| author_facet | Radouane Yafia |
| author_sort | Radouane Yafia |
| collection | DOAJ |
| description | This paper is devoted to the study of the stability of limit
cycles of a system of nonlinear delay differential equations with
a discrete delay. The system arises from a model of population
dynamics describing the competition between tumor and immune
system with negative immune response. We study the local
asymptotic stability of the unique nontrivial equilibrium of the
delay equation and we show that its stability can be lost through
a Hopf bifurcation. We establish an explicit algorithm for
determining the direction of the Hopf bifurcation and the
stability or instability of the bifurcating branch of periodic
solutions, using the methods presented by Diekmann et al. |
| format | Article |
| id | doaj-art-83a47149580b441ebf4afa1cea6561ec |
| institution | OA Journals |
| 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-83a47149580b441ebf4afa1cea6561ec2025-08-20T02:09:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/5846358463Stability of limit cycle in a delayed model for tumor immune system competition with negative immune responseRadouane Yafia0Département de Mathématiques et Informatique, Faculté des Sciences, Université Chouaib Doukkali, El Jadida BP 20, MoroccoThis paper is devoted to the study of the stability of limit cycles of a system of nonlinear delay differential equations with a discrete delay. The system arises from a model of population dynamics describing the competition between tumor and immune system with negative immune response. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lost through a Hopf bifurcation. We establish an explicit algorithm for determining the direction of the Hopf bifurcation and the stability or instability of the bifurcating branch of periodic solutions, using the methods presented by Diekmann et al.http://dx.doi.org/10.1155/DDNS/2006/58463 |
| spellingShingle | Radouane Yafia Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response Discrete Dynamics in Nature and Society |
| title | Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response |
| title_full | Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response |
| title_fullStr | Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response |
| title_full_unstemmed | Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response |
| title_short | Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response |
| title_sort | stability of limit cycle in a delayed model for tumor immune system competition with negative immune response |
| url | http://dx.doi.org/10.1155/DDNS/2006/58463 |
| work_keys_str_mv | AT radouaneyafia stabilityoflimitcycleinadelayedmodelfortumorimmunesystemcompetitionwithnegativeimmuneresponse |