On the Dynamics of a Higher-Order Rational Recursive Sequence

Abstract

In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence

\begin{equation*} x_{n+1}=ax_{n}+\dfrac{bx_{n-l}+cx_{n-k}}{dx_{n-l}+ex_{n-k}},\;\;\;n=0,1,..., \end{equation*}

where the parameters $a,b,c,d\;$and$\;e\;$are positive real numbers and the initial conditions $x_{-k},x_{-k+1},...,x_{-l},x_{-l+1},...,x_{-1}$ and $x_{0}\;$are positive real numbers.