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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 ›› 2023, Vol. 40 ›› Issue (2): 265-280.doi: 10.3969/j.issn.1005-3085.2023.02.007

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时间模上一类二阶延迟非线性非正则动态系统的动力学性质

张  萍1,   杨甲山2   

  1. 1. 邵阳学院理学院，湖南 邵阳 422004 
    2. 梧州学院大数据与软件工程学院，广西 梧州 543002
  • 收稿日期:2020-12-06 接受日期:2021-06-08 出版日期:2023-04-15 发布日期:2023-06-20
  • 通讯作者: 杨甲山 E-mail: syxyyjs@163.com
  • 基金资助:
    国家自然科学基金 (51765060)；湖南省教育厅一般项目 (20C1683).

Dynamical Properties of Certain Second-order Delay Nonlinear Noncanonical Dynamic Equations on Time Scales

ZHANG Ping1,   YANG Jiashan2   

  1. 1. School of Science, Shaoyang University, Shaoyang, Hunan 422004
    2. School of Data Science and Software Engineering, Wuzhou University, Wuzhou, Guangxi 543002
  • Received:2020-12-06 Accepted:2021-06-08 Online:2023-04-15 Published:2023-06-20
  • Contact: J. Yang. E-mail address: syxyyjs@163.com
  • Supported by:
    The National Natural Science Foundation of China (51765060); the Scientific Research Fund of Education Department of Hunan Province (20C1683).

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摘要：

时间模上的分析理论不仅有效地统一了连续分析和离散分析的理论，而且在理论和实际中都有着非常广泛的应用。时间模上中立型时滞动态系统的振动性与非振动性理论作为中立型动态系统定性理论中的重要内容，更是引起了学术界广泛兴趣和高度关注。针对时间模上一类二阶延迟非线性非正则动态系统的动力学性质展开研究，利用时间模上的微积分理论和广义的Riccati变换及各种分析技巧，在一定的条件下建立了该系统的两条新的动力学性质，进一步推广且改进了近年来已有的部分经典研究成果，并充分反映了时滞在系统振荡中的影响作用，最后给出了两个实例验证了新定理的有效性。

关键词: 振动性, 时间模, Emden-Fowler型动态系统, 阻尼项, 非线性

Abstract:

The analysis theory on the time scales not only effectively unifies the theory of continuous analysis and discrete analysis, but also becomes an indispensable mathematics tool in such domains of natural science and social science. Moreover, the oscillation and non-oscillation theories are the key issues of qualitative study of the neutral dynamic equations, which have attracted people's attention. Therefore, the dynamical properties of certain second-order delay nonlinear noncanonical dynamic equations on time scales are discussed. By using the calculus theory on the time scales and the generalized Riccati transformation and some necessary analytic techniques, two new dynamical properties for the equations under certain conditions are established. The results extend and improve the part of the results established in previous literatures. Finally, the effectiveness of the theoretical results are verified by two examples.

Key words: oscillation, time scales, Emden-Fowler dynamic equations, damping term, nonlinear

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