Bifurcation and Stability Analysis of a System of Fractional-Order Differential Equations for a Plant–Herbivore Model with Allee Effect

Yousef A., Bozkurt Yousef F.

MATHEMATICS, vol.7, no.5, pp.1-18, 2019 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 7 Issue: 5
  • Publication Date: 2019
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-18
  • Erciyes University Affiliated: Yes

Abstract

Abstract

This article concerns establishing a system of fractional-order differential equations (FDEs) to model a plant–herbivore interaction. Firstly, we show that the model has non-negative solutions, and then we study the existence and stability analysis of the constructed model. To investigate the case according to a low population density of the plant population, we incorporate the Allee function into the model. Considering the center manifold theorem and bifurcation theory, we show that the model shows flip bifurcation. Finally, the simulation results agree with the theoretical studies.