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The global attractivity of a higher order rational difference equation. (English) Zbl 1112.39002

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 1k1m 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.


MSC:
39A11Stability of difference equations (MSC2000)
39A20Generalized difference equations