Xianyi Li

MSC: | 39A10 | Difference equations, additive |

**Abstract:**
In this paper the dynamics for a third-order
rational difference equation is considered. The rule for the
trajectory structure of solutions of this equation is clearly
described out. The successive lengths of positive and negative
semicycles of nontrivial solutions of this equation are found to
occur periodically with prime period 7. And the rule is $3^+, 2^-,
1^+, 1^-$ in a period. By utilizing the rule, the positive
equilibrium point of the equation is verified to be globally
asymptotically stable.

karin.martin@uni-rostock.de

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