Dynamics of a Mathematical Model of Planthopper–Beetle Interactions for Conservation in Rice Field Ecosystems Using Holling Type II and Crowley–Martin Functional Responses

Abstract

Advances in science and technology have led to new ways of understanding how living things interact within ecosystems. One such method is the creation of mathematical models to explain the relationships and changes in population numbers in numerical terms. This study aims to create a model of the interaction between planthoppers, which are the main pests of rice plants, and beetles, which are natural predators of planthoppers. This model uses two types of response functions, namely Holling type II and Crowley–Martin, which describe how predators prey while considering the effects of satiation and interference between other predators. The analysis was conducted analytically and numerically to determine the equilibrium point, local stability, and the impact of parameter changes on population changes. The results show that the system has a stable positive equilibrium point under certain conditions. Variations in certain parameters can cause changes in population stability within the system. Models with two response functions (Holling Type II and Crowley-Martin) provide more realistic results than single models. This research contributes to the development of mathematical ecology models that provide a deeper understanding of predator-prey interactions and can serve as a basis for more effective pest population control in agricultural environments.