Bifurcation Analysis of a Plant-Herbivore Model Constructed with System of Difference Equations

Year 2018, , 237 - 247, 31.03.2018

Şenol Kartal

https://doi.org/10.21597/jist.407880

Abstract

In this study, a plant-herbivore mathematical model constructed with the system of difference

equation is considered. Using Center Manifold theorem, the eigenvalue assignment, transversality and nonresonance

conditions that required for the existence of Neimark Sacker bifurcation in the system are analyzed and it has been

theoretically shown that these conditions are satisfied. In order to show the accuracy of these theoretical conditions,

some parameter values have been determined and the bifurcation diagram and phase diagrams of the system have

been obtained for these parameter values.

Keywords

Neimark-Sacker bifurcation, plant-herbivore model, stability, system of difference equation

Fark Denklem Sistemleriyle Oluşturulmuş Ot-Otçul Modelinin Çatallanma Analizi

Abstract

Bu çalışmada, fark denklem sistemiyle oluşturulmuş bir ot-otçul matematiksel modeli göz önüne alınmıştır.

Center Manifold teoremi kullanılarak sistemde Neimark Sacker çatallanmasının oluşması için gerekli olan özdeğer

eşliği, transversality ve nonresonance koşulları analiz edilmiş ve teorik olarak bu koşulların sağlandığı gösterilmiştir.

Elde edilen bu teorik koşulların doğruluğunu göstermek için bazı parametre değerleri belirlenmiş ve bu parametre

değerleri için sistemin çatallanma diagramı, faz diyagramları elde edilmiştir.

Keywords

Fark denklem sistemi, kararlılık, Neimark-Sacker çatallanma, ot-otçul model

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