On stability analysis of higher-order rational difference equation (Q2004170)

Summary: In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence \(w_{n + 1}= w_{n - p}\left( \alpha + \left( \beta w_n / \gamma w_n + \delta w_{n - r}\right)\right)\), where \(\gamma w_n\neq-\delta w_{n - r}\) for \(r\in\left( 0 , \infty\right)\), \(\alpha,\beta,\gamma,\delta\in\left( 0 , \infty\right)\), and \(r>p\geq0\). With initial values \(w_{- p}, w_{- p + 1},\ldots, w_{- r}, w_{- r + 1},\ldots, w_{- 1},\text{ and } w_0\) are positive real numbers. Some numerical examples are given to verify our theoretical results.