Yixiang Hu
Xianyi Li
The paper is published:
Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq.
61, 73 - 83 (2006)
| 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.
Keywords: rational difference equation, semicycle, cycle length, global asymptotic
stability.
Notes: This work is supported by NNSF of China (grant: 10371040), Mathematical Tianyuan Foundation of
China (grant: TY10026002-01-05-03), Excellent Youth Project of Educational Committee of Hunan Province (grant: 04B056), the Foundation for "New Century '121'
Talents in Hunan Province" and the Foundation for
"Chief Professor of Mathematical Discipline in Hunan Province".
karin.martin@uni-rostock.de
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