Numerical methods for Competitive Hunters Model

Abstract

When two or more species compete with each other to gain the same limited resources, this situation is known as competition interaction or Competitive Hunters Model. In this study, we plot exact orbit and determine the pattern of behavior by using the Volterra mapping. We also test the accuracy of our numerical approximation methods. Selected numerical methods are Euler, Taylor Series and Runge-Kutta method to plot the orbit for this competitive model. The accuracy of determining the precise orbit and behavior patterns for Competitive Hunters Model for Runge-Kutta, Euler and Taylor Series methods will be studied. Exact orbit from Volterra mapping will be used as the control factor. Observation extended by taking data from experiment performed on P. Caudatum and P. Aurelia samples to observe the theory of competition between this two species when they interact. Base on competitive exclusion principle; exclusion often occurs at a slow rate, therefore it was difficult to determine if equilibrium and stability exist, however it depends on their initial condition and initial numbers of sample for those population that compete with each other. As a solution, we use numerical approximation methods and carrying capacity that we have obtained from curve fitting process as a predictive tool to determine which species will dominate the other species in this competitive hunters' situation.