Analytical Study of a System of Dierence Equation

We study the qualitative behavior of a predator-prey model, where the carrying capacity of thepredators environment is proportional to the number of prey. The considered system is given bythe following rational di erence equations:xn+1=xnyn2yn1+yn2;yn+1=ynxn2�xn1�xn2;n= 0;1;���;where the initial conditionsx2;x1;x0;y2;y1;y0are arbitrary positive real numbers. Also,we give speci c form of the solutions of some special cases of this equation. Some numericalexamples are given to verify our theoretical results.