Symmetry, reductions and exact solutions of the difference equation   $u_{n+2}=au_n/(1+bu_nu_{n+1})$
  We investigate the solutions of the second-order difference equation $u_{n+2}=(au_n)/(1+bu_nu_{n+1})$ using a group of transformations (Lie symmetries) that leaves the solutions invariant. 
Mensah Folly-Gbetoula
nlin.SI