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

Ali Yousef and Fatma Bozkurt Yousef
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Ali Yousef: Department of Mathematics, Kuwait College of Science and Technology, 27235 Kuwait City, Kuwait
Fatma Bozkurt Yousef: Department of Mathematics, Kuwait College of Science and Technology, 27235 Kuwait City, Kuwait

Mathematics, 2019, vol. 7, issue 5, 1-18

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.

Keywords: fractional-order differential equation; stability; flip bifurcation; Allee effect (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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