Global Stability of an Economic Model

In this paper, we investigate the global stability of the following economic system of difference equations { x(n+1) = (1 - alpha)x(n) + beta x(n)(1 - x(n))e(-(xn+yn)) y(n+1) = (1 - alpha)y(n) + beta y(n)(1 - y(n))e(-(xn+yn)) , n = 0, 1, ... , (I) where alpha, and beta is an element of (0, infinity) with the initial conditions x(0) and y(0) is an element of (0,infinity). First we study the global behavior of the following general system of difference equations X-n((1)) = phi(1)(x(n-s1)((1))(1), x(n-s1)((2)(2))), X-n((2)) = phi(2)(x(n-s2)((2))(2), x(n-s1)((3)(3))), X-n((3)) = phi(3)(x(n-s2)((3))(3), x(n-s1)((4)(4))), X-n((k)) = phi(k)(x(n-s2)((k))(k), x(n-s2)((1)(1))). for n is an element of N-o where s(1)((i)), S-2((i)) is an element of N-o for i = 1,2, ... , k, with positive initial conditions. Second we apply the obtained results to investigate the global stability of System (I).