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

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

Stability and Bifurcation Analysis of a Conformable Fractional Order Logistic Model with Piecewise Constant Arguments

In this study, a conformable fractional order logistic model with piecewise constant arguments is considered. A discrete system is obtained by applying a discretization process to the model based on the use of piecewise constant arguments. By using the Schur-Cohn criterion, necessary and sufficient condition is obtained for asymptotic stability of a positive equilibrium point of the discrete system. Moreover, bifurcation analysis shows that NeimarkSacker bifurcation occurs due to the change of parameter r in the system. In addition, effect of fractional order parameter ( ? ) and discretization parameter ( ℎ ) on the dynamic structure of the system are investigated. Finally, all theoretical results are supported by numerical simulations.

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