PM  >> Vol. 7 No. 5 (September 2017)

    时标上一类分布时滞线性动力方程的全局吸引性
    Global Attractivity for a Linear Dynamic Equation with a Distributed Delay on Time Scales

  • 全文下载: PDF(452KB) HTML   XML   PP.408-416   DOI: 10.12677/PM.2017.75053  
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作者:  

舒明春:集美大学 诚毅学院,福建 厦门;
黄振坤:集美大学 理学院,福建 厦门

关键词:
全局吸引性时标上分布时滞混合时滞线性动力方程Global Attractivity Distributed Delay on Time Scales Mixed Time Delays Linear Dynamic Equation

摘要:

本文研究时标上一类具有分布时滞的线性动力方程,利用Lyapunov函数方法,得到了该方程全局吸引性的一个充分条件,并且进一步分析了具有混合时滞的线性动力方程在时标上的全局吸引性。最后文章给出了几个例子予以说明。

In this paper, we consider a linear dynamic equation with a distributed delay on time scales. By using Lyapunov function method, we obtain a novel sufficient condition for global attractivity of the linear delayed dynamic equation. And the linear dynamic equation with mixed delays on time scales is also discussed. Some examples are given to illustrate our results.

文章引用:
舒明春, 黄振坤. 时标上一类分布时滞线性动力方程的全局吸引性[J]. 理论数学, 2017, 7(5): 408-416. https://doi.org/10.12677/PM.2017.75053

参考文献

[1] Bohner, M. (2002) and Peterson, A. Advances in Dynamic Equations on Time Scale. Birkhauser, Boston.
[2] Bohner, M. and Peterson, A. (2001) Dynamic Equations on Time Scales: An Introduction Applications. Birkhauser, Boston.
https://doi.org/10.1007/978-1-4612-0201-1
[3] Dahal, R. (2009) Dynamic Equations on Time Scales. Dissertations & Theses, Gradworks, 38, 253-256.
[4] Xu, Y.J. and Xu, Z.T. (2009) Oscillation Criteria for Two-Dimensional Dynamic Systems on Time Scales. Computational & Applied Mathematics, 225, 9-19.
https://doi.org/10.1016/j.cam.2008.06.010
[5] Yu, J.S. and Cheng, S.S. (1994) A Stability Criterion for a Neutral Difference Equation with Delay. Applied Mathematics Letters, 7, 75-80.
https://doi.org/10.1016/0893-9659(94)90097-3
[6] 周展, 李红娟. 一类时标上时滞动力方程的全局吸引性[J]. 广州大学学报(自然科学版), 2009, 8(6): 1-4.
[7] Tan, Y.X. and Huang, Z.K. (2016) Synchronization of Drive-Response Networks with Delays on Time Scales. IEEE/CAA Journal of Automatica Sinica, PP, 1-10.
[8] Matsumoto, A., Szidarovszky, F. and Yoshida, H. (2011) Dynamics in Linear Cournot Duopolies with Two Time Delays. Computational Economics, 38, 311-327.
https://doi.org/10.1007/s10614-011-9295-6
[9] Ruan, S.G. and Filil, R. (2004) Dynamics of a Two-Neuron System with Discrete and Distributed Delays. Physica D: Nonlinear Phenomena, 191, 323-342.
https://doi.org/10.1016/j.physd.2003.12.004
[10] 杨小婧, 陈斯养. 具有混合时滞血液模型的Hopf分支与数值分析[J]. 计算机工程与应用, 2010, 46(31): 139-142.
[11] Rudin, W. 数学分析原理[M]. 第3版. 北京: 机械工业出版社, 2004.