Some properties of the solutions of the difference equation x n + 1 = a x n + b x n x n − 4 c x n − 3 + d x n − 4

In this article, we study some properties of the solutions of the following difference equation: x n + 1 = a x n + b x n x n − 4 c x n − 3 + d x n − 4 , n = 0 , 1 , … where the initial conditions x − 4 , x − 3 , x − 2 , x − 1 , x 0 are arbitrary positive real numbers and a , b , c , d are positive constants. Also, we give specific form of the solutions of four special cases of this equation.