Qualitative behavior of a two-dimensional discrete-time plant-herbivore model

Abstract

An important area of study in mathematical ecology is the coexistence of populations of herbivores and plants. The plant-herbivore model is a dynamic relationship where plants serve as a basic food source for herbivores, whereas herbivores are essential in the formation of plant populations and communities. In this paper, we study the dynamical behavior of a discrete-time plant-herbivore model. Existence and stability of equilibria are studied. Moreover, we analyse the transcritical bifurcation of the proposed system using bifurcation theory. The Neimark-Sacker bifurcation is also shown. The bifurcation diagrams are presented. Finally, some numerical examples are provided to support our theoretical results. The used approaches are powerful and useful to be applied for more nonlinear models.