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dc.contributor.authorKayan, S.
dc.contributor.authorMerdan, Hüseyin
dc.contributor.authorYafia, R.
dc.contributor.authorGoktepe, S.
dc.date.accessioned2019-07-04T14:19:41Z
dc.date.available2019-07-04T14:19:41Z
dc.date.issued2017
dc.identifier.citationKayan, Ş., Merdan, H., Yafia, R., & Goktepe, S. (2017). Bifurcation analysis of a modified tumor-immune system interaction model involving time delay. Mathematical Modelling of Natural Phenomena, 12(5), 120-145.en_US
dc.identifier.issn0973-5348
dc.identifier.urihttps://doi.org/10.1051/mmnp/201712508
dc.identifier.urihttp://hdl.handle.net/20.500.11851/1671
dc.description.abstractWe study stability and Hopf bifurcation analysis of a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a reaction-diffusion system including time delay under the Neumann boundary conditions, and is based on Kuznetsov-Taylor's model. Choosing the delay parameter as a bifurcation parameter, we first show that Hopf bifurcation occurs. Second, we determine two properties of the periodic solution, namely its direction and stability, by applying the normal form theory and the center manifold reduction for partial functional differential equations. Furthermore, we discuss the effects of diffusion on the dynamics by analyzing a model with constant coefficients and perform some numerical simulations to support the analytical results. The results show that diffusion has an important effects on the dynamics of a mathematical model.en_US
dc.language.isoengen_US
dc.publisherEDP Sciencesen_US
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectHopf bifurcationen_US
dc.subjecttumor immune system competitionen_US
dc.subjectreaction-diffusion systemen_US
dc.subjectdelay differential equationsen_US
dc.subjectstabilityen_US
dc.subjectperiodic solutionsen_US
dc.titleBifurcation Analysis of a Modified Tumor-immune System Interaction Model Involving Time Delayen_US
dc.typearticleen_US
dc.relation.journalMathematical Modelling Of Natural Phenomenaen_US
dc.contributor.departmentTOBB ETU, Faculty of Science and Literature, Depertment of Mathematicsen_US
dc.contributor.departmentTOBB ETÜ, Fen Edebiyat Fakültesi, Matematik Bölümütr_TR
dc.identifier.volume12
dc.identifier.issue5
dc.identifier.startpage120
dc.identifier.endpage145
dc.identifier.wosWOS:000412852300008
dc.identifier.scopus2-s2.0-85031500791
dc.contributor.tobbetuauthorMerdan, Hüseyin
dc.contributor.YOKid125872
dc.identifier.doi10.1051/mmnp/201712508
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıtr_TR


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