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Bifurcation analysis of a modified tumor-immune system ınteraction model ınvolving time delay

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dc.contributor.author Kayan, Ş.
dc.contributor.author Merdan, H.
dc.contributor.author Yafia, R.
dc.contributor.author Göktepe, S.
dc.date.accessioned 2020-02-28T08:22:15Z
dc.date.available 2020-02-28T08:22:15Z
dc.date.issued 2017
dc.identifier.citation Kayan, S; Merdan,H; Yafia, R; Göktepe, S., "Bifurcation analysis of a modified tumor-immune system ınteraction model ınvolving time delay", Mathematical Modelling Of Natural Phenomena, Vol.12, No.5, pp.120-145, (2017). tr_TR
dc.identifier.issn 0973-5348
dc.identifier.uri http://hdl.handle.net/20.500.12416/2548
dc.description.abstract We 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. tr_TR
dc.language.iso eng tr_TR
dc.publisher EDP Sciences A. tr_TR
dc.relation.isversionof 10.1051/mmnp/201712508 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Hopf Bifurcation tr_TR
dc.subject Tumor Immune System Competition tr_TR
dc.subject Reaction-Diffusion System tr_TR
dc.subject Delay Differential Equations tr_TR
dc.subject Stability tr_TR
dc.subject Periodic Solutions tr_TR
dc.title Bifurcation analysis of a modified tumor-immune system ınteraction model ınvolving time delay tr_TR
dc.type article tr_TR
dc.relation.journal Mathematical Modelling Of Natural Phenomena tr_TR
dc.identifier.volume 12 tr_TR
dc.identifier.issue 5 tr_TR
dc.identifier.startpage 120 tr_TR
dc.identifier.endpage 145 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR


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