Dynamics of nonlinear difference equation $$x_{n+1}=\frac{\beta x_{n}+\gamma x_{n-k}}{A+Bx_{n}+C x_{n-k}}$$xn+1=βxn+γxn-kA+Bxn+Cxn-k
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DOI: 10.1007/s12190-017-1116-1
Abstract: The main goal of this paper is to investigate the boundedness, invariant intervals, semi-cycles and global attractivity of all nonnegative solutions of the equation $$\begin{aligned} x_{n+1}=\frac{\beta x_{n}+\gamma x_{n-k}}{A+Bx_{n}+C x_{n-k}},\quad n\in \mathbb {N}_0 , \end{aligned}$$xn+1=βxn+γxn-kA+Bxn+Cxn-k,n∈N0,where the… read more here.
Keywords: beta gamma; bxn cxn; frac beta;