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

Abstract

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.