Qualitative Behavior of Solutions of Tenth-Order Recursive Sequence Equation

Abstract

Most nonlinear difference equations have exact solutions that are not always possible to obtain theoretically. As a result, a large number of researchers investigate several qualitative aspects of difference equations in order to predict their lengthy behavior. The goal of our research is to obtain the solutions of a tenth-order difference equation $U_{n+1}=U_{n-9}{U}_{n-5}{U}_{n-1}/U_{n-7}{U}_{n-3}\left(\pm 1\pm U_{n-9}{U}_{n-5}{U}_{n-1}\right),n\ge 0$ , where the initial values are positive real numbers. Stability and periodicity are also investigated.