Karışık gecikmeli bir sinir ağı 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 karışık gecikmeli iki sinir hücresinin hareketini ifade eden bir sistem 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, a neural network model with mixed delays 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, a neural network model with mixed delays 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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Mixed delay, Hopf bifurcation, Stability, Periodic solution, Karışık gecikmeli diferansiyel denklem, Hopf çatallanma, Kararlılık, Periyodik çözüm