Global behavior of a fourth-order difference equation with quadratic term

In this paper, we determine the forbidden set, introduce an explicit formula for the solutions, and discuss the global behavior of solutions of the difference equation: x n + 1 = a x n x n - 2 - b x n + c x n - 3 , n = 0 , 1 , … where a , b , c are positive real numbers and the initial conditions x - 3 , x - 2 , x - 1 , x 0 are real numbers.