The dynamics of plant-herbivore interactions are essential for understanding ecosystem stability and resilience. This article investigated the effects of incorporating a harvesting effect on the dynamics of a discrete-time plant-herbivore system. An analysis was performed to determine the existence and stability of fixed points. In addition, studies have shown that the system experienced transcritical, period-doubling, and Neimark-Sacker bifurcations. Moreover, we provided numerical simulations to substantiate our theoretical results. Our research indicated that harvesting in excessive amounts may have negative effects on the populations of both plants and herbivores. However, when harvesting was done at moderate levels, it promoted the coexistence and stability of both populations. The findings of our analysis provided a deep understanding of the intricate dynamics of ecological systems and underscored the need to use sustainable harvesting methods for the management and preservation of ecosystems.

This study explores the dynamics of a discrete‐time predator–prey system, incorporating a Holling type III functional response and prey refuge, through the piecewise constant argument method. This method keeps things consistent and prevents negative population values, which is often a drawback of older techniques. We take a closer look at fixed points, exploring their existence and stability. We identify the conditions that lead to period‐doubling and Neimark–Sacker bifurcations, and we back up our findings with numerical simulations. Our findings emphasize how important the predation coefficient is for keeping ecological balance and show that, in this model setup, the refuge for prey has a minimal effect on the stability of the system. These insights help us better understand the relationships between predators and their prey, providing valuable guidance for conserving biodiversity and managing ecosystems.