一类特殊的三阶有理差分系统的动力学行为研究

摘要

In this paper,a special rational system of third-order difference is discussed.Firstly,we analyze the existence and stability of equilibria.It is showed that the trivial equilibrium is locally stable,and the positive equilibrium is unstable.Further,we consider the existence of prime period-two solutions.And the convergence rate from the solutions to the trivial equilibrium is studied.Finally,the results are verified by numerical simulations.%对一类特殊的三阶有理差分系统的定性行为进行了研究.利用差分方程的基本理论,考虑了系统中平衡点的存在性和稳定性;进而讨论了系统解的周期性问题,得到了阶-2周期解存在的条件,并分析了系统解序列收敛到平凡平衡点的收敛速度;最后,通过数值模拟验证了所得结论的正确性.