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

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  • Ma, Jian
  • Ma, Yixue
  • Fu, Qiuxia

Abstract

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.

Suggested Citation

  • Ma, Jian & Ma, Yixue & Fu, Qiuxia, 2026. "Applications of Schur-Cohn matrix and matrix pencil methods in studying the stability of high-dimensional neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 508(C).
    • Handle: RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003650
    DOI: 10.1016/j.amc.2025.129639
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