Dynamics of a higher-order nonlinear difference equation
Summary: We consider the higher-order nonlinear difference equation \[ x_{n+1}=\frac{\alpha +x_{n}}{A+Bx_{n}+x_{n - k}},\quad n=0,1,\dots, \] where the parameters are positive real numbers and the initial conditions \(x_{ - k},\dots ,x_{0}\) are nonnegative real numbers, \(k\geq 2\). We investigate the periodic character, the invariant intervals, and the global asymptotic stability of all positive solutions of the abovementioned equation. We show that the unique equilibrium of the equation is globally asymptotically stable under certain conditions.
higher-order nonlinear difference equation
scientific article; zbMATH DE number 5793497
scientific article