Dynamics of a plant-herbivore system with Ricker plant growth and the strong Allee effects on plant population

Abstract

We examine a discrete-time model of plant-herbivore interaction, in which the population of plants follows the Ricker law and is affected by strong Allee effects. We discuss the equilibrium points, including their characteristics and number. Additionally, we analyze in detail the local behavior of the solutions around the equilibrium points. Under certain initial conditions, both populations may go extinct. We conduct research demonstrating the occurrence of transcritical and period-doubling bifurcations, resulting in a stable two-cycle at the boundary equilibrium. However, the interior equilibrium becomes unstable due to the emergence of the Neimark-Sacker bifurcation and period-doubling. We confirm the latter's existence through analytical methods and illustrate the period-doubling bifurcation through numerical simulations.