Conformable Kesirsel Mertebeden Tam Değer Fonksiyonlu Lojistik Modelin Kararlılık ve Çatallanma Analizi

Year 2020, Volume: 9 Issue: 3, 1080 - 1090, 26.09.2020

Güven Kaya Senol Kartal

https://doi.org/10.17798/bitlisfen.665517

Cited By: 1

Abstract

Bu çalışmada, conformable kesirsel mertebeden tam değer fonksiyonlu lojistik model ele alınmıştır. Modele tam değer fonksiyonlarının kullanılmasına dayalı bir ayrıklaştırma işlemi uygulanılarak bir fark denklem sistemi elde edilmiştir. Elde edilen bu fark denklem sisteminin pozitif denge noktasının yerel asimptotik kararlı olmasını sağlayan cebirsel koşullar Schur-Cohn kriterlerinin kullanılmasıyla elde edilmiştir. Yine çatallanma analizi ile sistemde r parametresinin değişimine bağlı olarak Neimark-Sacker çatallanmasının oluştuğu gösterilmiştir. Ayrıca kesirsel mertebeden türev parametresi ( α ) ve kesiklileştirme parametresi ( h ) nin sistemin dinamik yapısı üzerindeki etkisi araştırılmıştır. Elde edilen tüm teorik sonuçlar nümerik simülasyonlarla desteklenmiştir.

Keywords

Conformable kesirli mertebeden türev, tam değer fonksiyonu, kararlılık, Neimark-Sacker çatallanma

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