Affiliation:
1. School of Mathematical Sciences, The National of University of Malaysia, 43600 Bangi, Selangor, Malaysia
2. Department of Basic Sciences, King Saud bin Abdulaziz University for Health Sciences, Riyadh 11426, Saudi Arabia
Abstract
We consider the higher order nonlinear rational difference equationxn+1=(α+βxn+γxn-k)/(A+Bxn+Cxn-k),n=0,1,2,…, where the parametersα,β,γ,A,B,Care positive real numbers and the initial conditionsx-k,…,x-1,x0are nonnegative real numbers,k∈{1,2,…}. We give a necessary and sufficient condition for the equation to have a prime period-two solution. We show that the period-two solution of the equation is locally asymptotically stable.
Subject
Applied Mathematics,Analysis