On the asymptotic stability of x_(n+1) = (a + x_nx_(n-k))/(x_n + x_(n-k))

摘要

We prove that the equilibrium solution of the rational difference equation x_(n+1)= (a+x_nx_(n-k))/(x_n+x_(n-k), n=0,1,2,... where k is a nonnegative integer, α≥0, and x_(-k),..., x_0 > 0, is globally asymptotically stable.