周期系数非线性差分方程的动力学性质  

Dynamic Properties of Nonlinear Difference Equation with Periodic Coefficients

作　　者：曹名圆[1] 杨月婷[1] 张晏毓 黄庆道[2] CAO Mingyuan;YANG Yueting;ZHANG Yanyu;HUANG Qingdao(College of Mathematics and Statistics,Beihua University,Jilin 132013,Jilin Province,China;Institute of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]北华大学数学与统计学院,吉林吉林132013 [2]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2020年第3期457-462,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11171131);吉林省科技厅自然科学基金(批准号:20180101221JC);吉林省科技发展计划项目(批准号:20180519011JH,20190303132SF);吉林省教育厅“十三五”科学技术项目(批准号:JJKH20200028KJ).

摘　　要：利用平衡点定义得到周期系数差分方程yn+1=Pn+Yn-1/Pn+Yn+Yn-2/Yn,n=0,1,2,…的平衡点,并研究其平衡点的周期性和稳定性,其中{p_n}是实的二周期序列.首先,在整个空间上讨论该方程的解,得到其二周期解、无界解,并给出不动点(平衡点和二周期解)的稳定性;其次,数值模拟该方程解的吸引域.结果表明,该方程平衡点和二周期解的稳定性受周期系数取值的影响.By using the definition of the equilibrium point,we obtain the equilibrium point of the following difference equation with periodic coefficients:yn+1=Pn+Yn-1/Pn+Yn+Yn-2/Yn,n=0,1,2,…and study the periodicity and the stability of the equilibrium point,where the sequences{p_n}consists real numbers of 2-period.Firstly,we discuss solutions of the equation in the whole space,obtain the 2-periodic and unbounded solutions of the difference equation,and give the stability of the fixed points(equilibrium point and 2-periodic solutions).Secondly,we simulate the basin of attraction of solutions of the difference equation.The results show that the stability of the equilibrium point and 2-periodic solutions of the difference equation is affected by the value of periodic coefficient.

关 键 词：差分方程 二周期系数 周期解 无界解 稳定性 

分 类 号：O175[理学—数学]