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

Fark Denklem Sistemleriyle Oluşturulmuş Ot-Otçul Modelinin Çatallanma Analizi

Abstract

In this study, a plant-herbivore mathematical model constructed with the system of differenceequation is considered. Using Center Manifold theorem, the eigenvalue assignment, transversality and nonresonanceconditions that required for the existence of Neimark Sacker bifurcation in the system are analyzed and it has beentheoretically 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 havebeen obtained for these parameter values.

Özet

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

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