Stability and numerical analysis for delay differential equations

时滞微分方程的稳定性和数值分析

• 批准号: 20540137
• 负责人: ISHIWATA Emiko
• 金额: $ 2.5万
• 依托单位: Tokyo University of Science
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540137/
• 关键词: 遅延微分方程式; 数値解析; 大域安定性; 数理生物モデル; 微分差分方程式; 離散型病理モデル; Lotka-Volterraモデル; 固有値計算; 離散型SIRモデル; 大域漸近安定性; パーマネンス; 固有値; 関数微分方程式; 大域的安定性

We obtained some results related to the functional differential equations by this grant. We first derived new global stability conditions for a class of difference equations with time delay. Next, we showed an attainable order of collocation methods for delay differential and Volterra integral equations with proportional delay. Super attainable order was also considered. Finally, we considered some global stability for epidemic models with time delay. Using a discretization of combined explicit with implicit schemes, we obtained the global dynamics of a discretized SIRS epidemic model with time delay, corresponding to that of continuous model.

利用这一资助，我们得到了一些与泛函微分方程有关的结果。首先给出了一类时滞差分方程新的全局稳定性条件。其次，我们给出了具有比例延迟的延迟微分和沃尔泰拉积分方程的配置方法的可达阶。超级可实现的秩序也被考虑在内。最后，我们考虑了一类具有时滞的传染病模型的全局稳定性。利用显式和隐式相结合的离散化方法，得到了离散化的具有时滞的SIRS传染病模型的全局动力学解，该解与连续模型的全局动力学解相对应。

项目成果

ホームページ等。

主页等

The discrete hungry Lotka–Volterra system and a new algorithm for computing matrix eigenvalues

• DOI: 10.1088/0266-5611/25/1/015007
• 发表时间: 2008
• 期刊: Inverse Problems
• 影响因子: 2.1
• 作者: A. Fukuda;E. Ishiwata;M. Iwasaki;Yoshimasa Nakamura

A Bäcklund transformation between two integrable discrete hungry systems

• DOI: 10.1016/j.physleta.2010.11.029
• 发表时间: 2011-01
• 期刊: Physics Letters A
• 影响因子: 2.6
• 作者: A. Fukuda;Yusaku Yamamoto;M. Iwasaki;E. Ishiwata;Yoshimasa Nakamura

Global dynamics of a discretized SIRS epidemic model with time delay

• DOI: 10.1016/j.jmaa.2010.05.007
• 发表时间: 2010-11-01
• 期刊: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
• 影响因子: 1.3
• 作者: Sekiguchi, Masaki;Ishiwata, Emiko
• 通讯作者: Ishiwata, Emiko

On collocation methods for delay differential and Volterra integral equations with proportional delay

• DOI: 10.1007/s11464-009-0004-x
• 发表时间: 2009-02
• 期刊: Frontiers of Mathematics in China
• 作者: E. Ishiwata;Y. Muroya