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