A predator prey model with Fuzzy initial populations

Abstract

The aim of this paper is to study a predator-prey population model which takes into account the uncertainty that arises when determining the initial populations of predator and prey. This model is solved numerically by means of a 4th-order Runge-Kutta method. Simulations are made and a graphical representation is also provided to show the evolution of both populations over time. In addition to that, a new phase-plane in this fuzzy setting, referred to as fuzzy phase-plane, is introduced. The stability of the equilibrium points is also described. Finally, this paper points out a new research direction on fuzzy dynamical systems, especially in non-linear cases.