一类三阶差分方程的周期轨及其稳定性和吸引性

The Periodic Orbits and Its Stability & Attractiveness of Some 3-order Difference Equations

通过变量代换得到三阶差分方程xn+1=xxnnxn+-1xn+-2a,a>0,x-2,x-1,x0>0,n=0,1,2,…的等价形式,把该三阶差分方程等价地化为一个三维一阶差分方程,并定义此三维一阶差分方程为映射T,通过映射T的局部线性化研究了该三阶差分方程的1周期和2周期轨道的存在性、稳定性及其吸引性.

In this paper,we obtain the equivalent modality of the 3-order difference equation xn＋1=xnxn-1＋α/xn＋xn-2,α〉0,x-2,x-1,x0〉0,n=0,1,2,… via variable＇s substitute.Then we turn it to a 3-dimension one order equation equivalently and name the 3-dimension one order equation map T.Finally,we utilize map T＇s local linearization to investigate existence,stability and attractiveness of 1-periodic orbit and 2-periodic orbits of 3-order difference equation.