Find in Library

We study the difference equation xn=[(f×g1+g2+h)/(g1+f×g2+h)](xn−1,…,xn−r), n=1,2,…, x1−r,…,x0>0, where f,g1,g2:(R+)r→R+ and h:(R+)r→[0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui}≤f(u1,…,ur)≤max1≤i≤r{ui,1/ui},(u1,…,ur)T∈(R+)r. We prove that this difference equation admits c=1 as the globally asymptotically stable equilibrium. This result extends and generalizes some previously known results.