Dynamical properties of a class of higher-order nonlinear difference equations

摘要

In this note, we consider the dynamical properties of the following higher-order nonlinear difference equationxn=∏i=1vxn-iβi+1+∏i=1vxn-iβi-1∏i=1vxn-iβi+1-∏i=1vxn-iβi-1,n=0,1,⋯with x−v, x−v+1, … , x−1 ∈ (0, ∞), β1 ∈ (0, 1], βi ∈ (0, +∞)(i = 2, 3, … , v). Our result extends and includes corresponding results in the recent literatures.