Qualitative behavior of difference equation of order two

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper we deal with the qualitative behavior of the solutions of the following difference equation x n+1 = ax n + bx 2 n cx n + dx n−1 , where the initial conditions x −1 , x 0 are arbitrary positive real numbers and a, b, c, d are positive constants. Also, we obtain the form of the solution of some special cases of this equation.