On the Dynamics of a Higher-Order Rational Difference Equation

The aim of this paper is to investigate the global asymptotic stability and the periodic character for the rational difference equation xn+1=αxn-1/(β+γΠi=lkxn-2ipi),  n=0,1,2,…, where the parameters α,β,γ,pl,pl+1,…,pk are nonnegative real numbers, and l,k are nonnegative integers such that l≤k