一类非线性时滞离散系统的渐近行为  

ASYMPTOTIC BEHAVIOR OF NONLINEAR DELAYED DISCRETE SYSTEMS

作　　者：洪宇 宋兴传 田艳玲 HONG Yu;SONG Xing-chuan;TIAN Yan-ling(School of Mathematics,South China Normal University,Guangdong 510631,China)

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《数学杂志》2023年第2期135-150,共16页Journal of Mathematics

基　　金：Supported by Natural Science Foundation of Guangdong Province(2020A1515010445)。

摘　　要：本文研究了一类二维时滞非线性差分系统.利用稳定性理论和最优控制理论等方法,本文首先获得了保证正平衡点的存在唯一以及全局渐近稳定的充分条件;然后对消费函数的最大化的最优控制问题进行讨论,获得了最优解的存在性与稳定性条件;最后,通过数值模拟验证了结果的有效性.本文推广了一维时滞非线性差分系统中给出的相关结论.In this paper,we consider a two-dimensional vector nonlinear difference system with time delay.By using stability theory and optimal control theory,sufficient conditions for the global asymptotic stability of a unique positive equilibrium are obtained.For the associated optimal control problem of maximizing the consumption functional,the existence of optimal solutions is established as well as their stability.Finally,numerical simulation is carried out to illustrate the validity of our results.Our results generalize the corresponding results on a one-dimensional vector nonlinear difference system.

关 键 词：时滞差分系统 全局渐近稳定 最优控制方法 

分 类 号：O175.7[理学—数学]