Asymptotic behavior of a new class of nonlinear rational difference equations

Abstract

This paper is concerned with the asymptotic behavior of solutions of a new class of the nonlinear rational difference equations. We establish new criteria for stability (local and global) and boundedness of solutions of the studied equation. Moreover, we investigate the periodic character (periodic two and three) of the solutions of these equations, by using new techniques. Finally, we give some interesting examples in order to verify our results.