DYNAMICS AND GLOBAL BEHAVIOR FOR A FOURTH-ORDER RATIONAL DIFFERENCE EQUATION

Abstract

In this paper we study the behavior of the rational difference equationof the fourth orderx n+1 = ax n + bx n x n−2 cx n−2 + dx n−3 , n = 0, 1, ...,where the initial conditions x−3 , x −2 , x −1 , x are arbitrary positive realnumbers and a, b, c, d are positive constants. Also, we give the solutionof some special cases of this equation.