基于级数研究一类离散动力系统的收敛性  

Studying the Convergence of a Class of Discrete Dynamical Systems Based on Series

作　　者：冯豪 

机构地区：[1]宜春学院数学与计算机科学学院,江西 宜春

出　　处：《应用数学进展》2024年第8期3865-3870,共6页Advances in Applied Mathematics

摘　　要：本文讨论了离散动力系统{ xn+1=xn+xnqnp0≤x11的收敛性。应用级数理论,给出了系统收敛的两个充分条件。当1p=q时,该动力系统是收敛的;当0pq且q>1时,该动力系统是收敛的。为更好解释相关理论,以24年阿里巴巴全球数学竞赛决赛的一道试题进行实例分析。同时,通过数值模拟的方式进一步验证了理论的正确性。The article discusses the convergence of the system { xn+1=xn+xnqnp0≤x11. By applying series theory, two sufficient conditions for the system convergence are provided: condition 1p=qensures convergence, while condition 0pqand q>1guarantees convergence. To better illustrate these theories, a problem from the finals of the 24th Alibaba Global Mathematics Competition is analyzed as a case study. Additionally, the correctness of the theory is further validated through numerical simulations.

关 键 词：动力系统 级数 收敛性 

分 类 号：O17[理学—数学]