Bir tümör-bağışıklık modeli için Hopf çatallanma ve kararlılık analizi
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2014-04
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Bahçeşehir Üniversitesi Fen Bilimleri Enstitüsü
Abstract
Bu tezde gecikmeli bir tümör-bağışıklık sisteminin dinamiği incelenmiş ve τ gecikme parametresi, çatallanma parametresi olarak seçilerek kararlılık ve Hopf çatallanma analizi çalışılmıştır. Ayrıca normal form teori ve Center Manifold teoremi kullanılarak kritik τ değerinde çatallanan periyodik çözümün yönü, kararlılığı ve periyodu elde edilmiştir.
In this thesis, the dynamics of a delayed tumor-immune system is investigated and by choosing time delay τ as bifurcating parameter, the stability and Hopf bifurcation analysis are studied. Moreover, by using normal form theory and center manifold theorem, the direction, stability and the period of the bifurcating periodic solution at critical values τ are obtained.
In this thesis, the dynamics of a delayed tumor-immune system is investigated and by choosing time delay τ as bifurcating parameter, the stability and Hopf bifurcation analysis are studied. Moreover, by using normal form theory and center manifold theorem, the direction, stability and the period of the bifurcating periodic solution at critical values τ are obtained.
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Keywords
Tumor-immune system, Delayed differential equation, Hopf bifurcation, Stability, Tümör-bağışıklık sistemi, Gecikmeli diferansiyel denklem, Hopf çatallanma, Kararlılık.