一类高阶有理差分方程的动力学定理  

DYNAMICAL THEOREMS FOR A CLASS OF HIGHER ORDER RATIONAL DIFFERENCE EQUATIONS

作　　者：全卫贞 王丽 周敬人 黄日娣 刘付滢 吴语桐 胡可满 QUAN Weizhen;WANG Li;ZHOU Jingren;HUANG Ridi;LIU Fuying;WU Yutong;HU Keman(Department of Mathematic,Zhanjiang Preschool Education College,Zhanjiang,Guangdong 524037,China;College of Basic Education,Lingnan Normal University,Zhanjiang,Guangdong 524037,China)

机构地区：[1]湛江幼儿师范专科学校数学系,广东湛江524037 [2]岭南师范学院基础教育学院,广东湛江524037

出　　处：《井冈山大学学报（自然科学版）》2024年第4期7-12,共6页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(11761011);广东大学生科技创新培育专项(pdjh2024b677);校级重点项目(ZY24CGZD01)。

摘　　要：根据差分方程理论,证明了高阶有理差分方程χ_(n+1)=A+Bχ_(n)/3的5个动力学定理,即唯一的正平衡解x的局部渐近稳定性、全局渐近稳定性、有界性、持续性、周期解与半循环长度等不同结论。并用计算机Matlab程序描绘此差分方程解的图像,进一步验证了这5个定理。According to the theory of difference equations,we prove five dynamic theorems for rational difference equationsχ_(n+1)=A+Bχ_(n)/3,including locally asymptotically stability,global asymptotically stability,boundedness,persistence,periodic solution,and semi-cycle length of the unique positive equilibrium solution.Then we used Matlab's numerical calculations to obtain the graph of the solution to the difference equation,which more intuitively verified the correctness of these 5 theorems.

关 键 词：差分方程 平衡解 渐近稳定性 有界性 半循环长度 

分 类 号：O175.7[理学—数学]