The global attractivity of a higher order rational difference equation
Concerning the difference equation \(y_n= f(y_{n-k}, y_{n-1},y_{n-m})\) with \[ f(x,y,z)= (xyz+ x+ y+ z)/(1+ xy+ xz+ yz) \] and \(1\leq k\leq 1\leq m\) the authors prove that every positive solution converges to \(1\). Moreover, for small \(k\), \(l\), \(m\) the semi-cycle structure of the solutions is pointed out.
scientific article; zbMATH DE number 5125945
scientific article