Schur-Cohn矩阵和矩阵铅笔法在高维中立型时滞微分方程稳定性研究中的应用

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-07-23 DOI:10.1016/j.amc.2025.129639

Jian Ma , Yixue Ma , Qiuxia Fu

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引用次数: 0

摘要

本文将为求解一般高维中立型时滞微分方程在何时何地保持稳定提供一种新的方法。利用Schur-Cohn矩阵、矩阵铅笔和广义特征值，将给出所有虚轴特征值，并以直接的方式确定临界延迟。此外，还将介绍一个简单的基于matlab的算法。本文的主要贡献是提供了一种确定一般高维实系数中立型时滞微分方程的虚轴特征值和最小时滞余量的计算方法。

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Applications of Schur-Cohn matrix and matrix pencil methods in studying the stability of high-dimensional neutral delay differential equations

This note will provide a novel method for figuring out when and where the generic high-dimensional neutral delay differential equations can keep stable. Using the Schur-Cohn matrices, matrix pencils, and generalized eigenvalues, all imaginary axis eigenvalues will be presented and the critical delays will be determined in a straightforward manner. Additionally, a simple MATLAB-based algorithm will be presented. The main contribution of this paper is that we provide a computational method for determining imaginary axis eigenvalues and minimal delay margin on general high-dimensional neutral delay differential equations with real coefficients.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.