Asymptotic Stability for a Class of Nonlinear Difference Equations

Abstract EN

We study the global asymptotic stability of the equilibrium point for the fractional difference equation xn+1=(axn-lxn-k)/(α+bxn-s+cxn-t), n=0,1,…, where the initial conditions x-r,x-r+1,…,x1,x0 are arbitrary positive real numbers of the interval (0,α/2a),l,k,s,t are nonnegative integers, r=max{l,k,s,t} and α,a,b,c are positive constants.

Moreover, some numerical simulations are given to illustrate our results.