Asymptotic Behavior of Equilibrium Point for a Class of Nonlinear Difference Equation

Abstract

We study the asymptotic behavior of the solutions for the following nonlinear difference equation xn+1=∑i=1sAkixn−ki/(B0+∑j=1tBljxn−lj),n=0,1,…, where the initial conditions x−r,x−r+1,…,x1,x0 are arbitrary nonnegative real numbers, k1,…,ks,l1,…,lt are nonnegative integers, r=max{k1,…,ks,l1,…,lt}, and Ak1,…,Aks,B0,Bl1,…,Blt are positive constants. Moreover, some numerical simulations to the equation are given to illustrate our results.