A New Prey-Predator Modeling with Experimental Data for Biological Control of Couch Grass

In this study, a new three-dimensional predator–prey model is developed, consisting of one prey and two predators. The aim of the model is to reduce or eliminate the target weed species through natural means. One of the novelties of the study is that one of the predators is the radish plant, and the model parameters are obtained from real data. The primary objective of the study is to investigate the natural suppression or eradication of the harmful weed species using the constructed predator–prey framework, supported by numerical simulations. Through these simulations, the interactions between two populations are examined by varying the initial planting rates/numbers of radish and couch grass, and the dynamic changes of the populations over time are analyzed. Furthermore, the model and its solutions are interpreted within the context of mathematical biology. The equilibrium points are determined, followed by numerical solutions of the three-dimensional system, and corresponding simulations are performed. The numerical simulations are carried out using the fourth-order Runge–Kutta method.