A Runge-Kutta numerical scheme applied in solving predator-prey fuzzy model with Holling type II functional response

Abstract

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The predator-prey model has been extensively studied, but only studies models 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.

Keywords

• predator-prey fuzzy model
• Holling type II functional response
• fuzzy parameter
• fuzzy initial population
• Zadeh extension principle
• 5th order Runge-Kutta method