Kajian Model Dinamik Predator-Prey untuk Keberlanjutan Tumbuhan terhadap Gangguan Herbivora

Abstract

The Holling Type II functional response in this study is used to analyze the interaction between plants as prey and herbivores as predators. The mathematical model utilized is based on the extended Lotka-Volterra equations to better reflect real ecosystem conditions. Numerical simulations were conducted to understand the dynamics of the populations of these two species over a specific time range. The parameters used include the growth rate of plants, the mortality rate of herbivores, environmental carrying capacity, and the efficiency of converting prey into predators.Through the modified Lotka-Volterra model with Holling Type II functional response, an equilibrium point was identified at (0.8039,0.9967), where the populations of plants and herbivores can coexist. This point indicates a condition where both populations are in a dynamic equilibrium. Furthermore, from the eigenvalue analysis conducted, it was found that λ^₁≈ 0,0714−0,7524i and λ₂≈ 0,0714+0,7524i indicating that the equilibrium point E^₂is classified as a spiral poin unstablet. The stability of this system suggests that the populations of plants and herbivores will not stabilize at this equilibrium point. The research indicates that the Lotka-Volterra model with Holling Type II functional response successfully predicts the dynamics of plant-herbivore interactions; however, the limited predation efficiency of herbivores leads to long-term imbalances. Therefore, appropriate ecosystem management strategies are necessary to prevent the collapse of herbivore populations and maintain the sustainability of plants within the ecosystem. This study provides important insights for mathematical model-based ecosystem management.