PREY-PREDATOR MODELS STABILITY WITH LESLIE-GOWER STRUCTURES IN PREY

Abstract

Along with the development of technology so rapidly the development of knowledge about dynamic systems is also growing rapidly.This aims tostudy find out the stability of prey-predator model using Leslie-Gower from with stages of structure on prey. Issues raised in the research are how to generate a mathematical model of the modification of Leslie-Gower prey-predator system with the response function of Holling type II; how to determine the point of equilibrium and stability analysis on a modified model of Leslie-Gower prey-predator with the response function of Holling type II; the effects of changes in the parameters on the actual state of the modification of Leslie-Gower prey-predator model with the response function og Holling type II; and the numerical simulation of the modification of Leslie-Gower prey-predator model with the response function oh Holling type II using the maple software. The problem was analysed based on a literature review. The steps used were: generating a mathematical model from the modification of Leslie-Gower prey-predator model with the response function of Holling type II; determine all fixed point; determine a cracteristic equation and the eigen value of jacobian matriks; determine in the value of the parameter of Hoft bifurcation; calculate the transversal angles; createa numerical simulation of the modification of Leslie-Gower prey-predator model with the response function of Holling type II using the software Maple; and drawing the conclusion.The results of the research show a model as follows: