Abstract
This paper is devoted to investigate the global behavior of the following rational difference equation: y(n+1) = alpha y(n-t)/(beta + gamma Sigma(k)(i=0)y(n-(2i+1))(p) Pi(k)(i=0)y(n-(2i+1))(q)), n = 0,1,2, . . ., where alpha, beta, gamma, p, q is an element of (0, infinity) and k, t is an element of {0, 1, 2, . . .} with the initial conditions x(0), x(-1),..., x(-2k), x(-2max{k, t}-1) is an element of (0,infinity). We will find and classify the equilibrium points of the equations under studying and then investigate their local and global stability. Also, we will study the oscillation and the permanence of the considered equations.