Stability and bifurcation analysis of a discrete-time plant-herbivore model with chaotic dynamics under weak Allee effect on plant

In this paper, we propose a discrete-time plant-herbivore model incorporating the weak Allee effect on plant populations to investigate the complex dynamics of ecological interactions. The model is formulated with two state variables representing plant and herbivore populations, alongside key parameters such as the plant’s intrinsic growth rate, herbivore death rate, and the weak Allee effect. Through both analytical and numerical approaches, we explore the local stability of equilibrium points, including trivial, boundary, and interior equilibria. The system exhibits rich dynamical behavior, including transcritical bifurcation, period-doubling bifurcation, and chaotic dynamics, as key parameters are varied. Numerical simulations validate the theoretical predictions, providing insights into how the weak Allee effect influences population stability and oscillatory dynamics. These findings have significant implications for ecological management strategies aimed at maintaining ecosystem stability and preventing overgrazing by herbivores.