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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 42 ›› Issue (6): 1014-1028.doi: 10.3969/j.issn.1005-3085.2025.06.003cstr: 32411.14.cjem.CN61-1269/O1.2025.06.003

• • 上一篇    下一篇

非线性多变时滞动力系统的稳定性及其仿真

王春生1,   李永明2,   冯炜彤3,   陈 含4   

  1. 1. 铜陵学院经济学院，铜陵  244061

    2. 上饶师范学院数学与计算机科学学院，上饶 334001

    3. 西安交通大学生命科学与技术学院，西安 710049

    4. 香港中文大学(深圳)数据科学学院，深圳 518172

  • 收稿日期:2022-11-17 接受日期:2023-04-27 出版日期:2025-12-15 发布日期:2026-02-15
  • 基金资助:
    国家自然科学基金 (12161074; 11461057)；江西省自然科学基金 (20212ACB201006)；广东省自然科学基金 (2016A030313542)；广东省普通高校特色创新项目(自然科学)(2018KTSCX339)；广东省教育科学规划课题(高等教育专项)(2022GXJK085).

Stability and Simulation of Nonlinear Multivariable Dynamical Systems with Time-delay

WANG Chunsheng1,  LI Yongming2,  FENG Weitong3,  CHEN Han4   

  1. 1. School of Economics, Tongling University, Tongling 244061
    2. School of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001
    3. School of Life Science and Technology, Xi'an Jiaotong University, Xi'an 710049
    4. School of Data Science, the Chinese University of Hong Kong, Shenzhen 518172
  • Received:2022-11-17 Accepted:2023-04-27 Online:2025-12-15 Published:2026-02-15
  • Supported by:
    The National Natural Science Foundation of China (12161074; 11461057); the Natural Science Foundation of Jiangxi Province (20212ACB201006); the Natural Science Foundation of Guangdong Province (2016A030313542); the General University Characteristic Innovation Project of Guangdong Province (Natural Science) (2018KTSCX339); the Guangdong Education Science Planning Project (Higher Education Special) (2022GXJK085).

摘要：

利用不动点方法给出了一类非线性多变时滞广义Halanay不等式零解的渐近稳定性定理。此项研究是不动点方法在Halanay不等式稳定性研究上的一次尝试，研究结果显示，利用不动点方法研究Halanay不等式的稳定性相比其他方法在某种情形下具有一定的优越性。根据时滞系统系数的不同特征，证明过程中引入相对应的函数来构造算子，使得结论更加灵活可行。之后，将所得成果应用于研究神经网络系统的稳定性，得到较好的结论。结合案例的数值模拟仿真结果验证了结论的准确性和优越性。此项研究为Halanay不等式稳定性的研究增添了新方法新思路，丰富了不动点方法的应用领域。

关键词: Halanay不等式, 仿真, 渐近稳定性, Banach不动点方法, Grossberg-Hopfield神经网络

Abstract:

In this paper, asymptotic stability theorems for zero solutions of a class of nonlinear multivariate time-lagged generalized Halanay inequalities are given using the fixed point method. This study is an attempt of the fixed point method in the study of the stability of Halanay inequalities, and the results show that the use of the fixed point method to study the stability of Halanay inequalities has certain superiority compared with other methods in certain situations. According to the different characteristics of time lag system coefficients, the proof process of this paper introduces the corresponding functions to construct the operator, which makes the conclusion more flexible and feasible. After that, the obtained results are applied to study the stability of neural network systems in this paper, and better conclusions are obtained. The numerical simulation results combined with the cases verify the accuracy and superiority of the conclusions of this paper. This study adds new methods and new ideas to the study of the stability of Halanay inequalities and enriches the application area of the fixed point method.

Key words: Halanay inequality, simulation, asymptotic stability, Banach fixed point method, Grossberg-Hopfield neural network

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