Solution and Attractivity for a Rational Recursive Sequence

Abstract

This paper is concerned with the behavior of solution of the nonlinear difference equation x n +1 = a x n −1 + b x n x n −1 /( c x n + d x n −2 ), n = 0, 1, …, where the initial conditions 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 solution of four special cases of this equation.