| 一类高阶有理差分方程的动力学定理 |
| |
| 引用本文： | 全卫贞,王丽,周敬人,黄日娣,刘付滢,吴语桐,胡可满. 一类高阶有理差分方程的动力学定理[J]. 井冈山大学学报(自然科学版), 2024, 45(4): 7-12 |
| |
| 作者姓名： | 全卫贞 王丽 周敬人 黄日娣 刘付滢 吴语桐 胡可满 |
| |
| 作者单位： | 湛江幼儿师范专科学校数学系, 广东, 湛江 524037;岭南师范学院基础教育学院, 广东, 湛江 524037 |
| |
| 基金项目： | 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xn+1=A+B×xn/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。
|
| 关 键 词： | 差分方程 平衡解 渐近稳定性 有界性 半循环长度 |
| 收稿时间： | 2024-03-06 |
| 修稿时间： | 2024-04-28 |
DYNAMICAL THEOREMS FOR A CLASS OF HIGHER ORDER RATIONAL DIFFERENCE EQUATIONS |
| |
| QUAN Weizhen,WANG Li,ZHOU Jingren,HUANG Ridi,LIU Fuying,WU Yutong,HU Keman. DYNAMICAL THEOREMS FOR A CLASS OF HIGHER ORDER RATIONAL DIFFERENCE EQUATIONS[J]. Journal of Jinggangshan University(Natural Sciences Edition), 2024, 45(4): 7-12 |
| |
| Authors: | QUAN Weizhen WANG Li ZHOU Jingren HUANG Ridi LIU Fuying WU Yutong HU Keman |
| |
| Affiliation: | Department of Mathematic, Zhanjiang Preschool Education College, Zhanjiang, Guangdong 524037, China;College of Basic Education, Lingnan Normal University, Zhanjiang, Guangdong 524037, China |
| |
| Abstract: | According to the theory of difference equations, we prove five dynamic theorems for rational difference equations xn+1=A+B×xn/x3n-m, 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. |
| |
| Keywords: | difference equation equilibrium point asymptotically stable boundedness semi-cycle length |
|
| 点击此处可从《井冈山大学学报(自然科学版)》浏览原始摘要信息 |
|
点击此处可从《井冈山大学学报(自然科学版)》下载免费的PDF全文 |
|
