You're viewing this item in the new Europeana website. View this item in the original Europeana.

Global behavior of a third order rational difference equation

In this paper, we determine the forbidden set and give an explicit formula for the solutions of the difference equation xn+1 = axnxn−1 ⁄−bxn + cxn−2 , n ∈ N0 where a, b, c are positive real numbers and the initial conditions x−2, x−1, x0 are real numbers. We show that every admissible solution of that equation converges to zero if either a < c or a > c with (a − c)/b < 1. When a > c with (a − c)/b…