Yixiang Hu
Xianyi Li

Dynamics of a Nonlinear Difference Equation

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".

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