A Runge-Kutta numerical scheme applied in solving predator-prey fuzzy model with Holling type II functional response - Sukarsih, I.; Supriatna, A. K.; Carnia, E.; Anggriani, N. (Frontiers in Applied Mathematics and Statistics, 2023)
The predator-prey model is a model of interaction between species expressed in the form of a system of differential equations that describes the dynamic relationship between prey and predator. This model was first introduced by Lotka in 1925 and Volterra in 1926. Various modifications of the predator-prey model have been made ever since, including the functional response modifications. However, mainly it only studies the model in a certain environment, where all parameters and initial values involved in the model are assumed to be certain. In real practice, some parameters and initial values are often uncertain. To overcome this uncertainty problem, a model can be made by using a fuzzy theoretical approach. In this paper, we develop a numerical scheme for solving two predator-prey models with a Holling type II functional response by considering fuzzy parameters and initial populations. The behavior of the model was studied qualitatively using the 5th order Runge-Kutta method of which was modified for the fuzzy system using the Zadeh extension principle. The numerical simulation results show that, when the initial populations of prey and predators are fuzzy, the behavior of the fuzzy model would be qualitatively the same as the crisp model. Finally, we conclude that the resulting fuzzy behavior represents a generalization of crisp behavior. This gives more realistic results since the solution is obtained by explicitly considering the problem of uncertainty.