Carleman linearization of nonlinear systems with centers: Spectra and Jordan basis

IF 4.3 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration Pub Date : 2025-03-24 DOI:10.1016/j.jsv.2025.119065

Tamás Kalmár-Nagy, Csanád Árpád Hubay

引用次数: 0

Abstract

We present the application of Carleman linearization to analyze the behavior of two-dimensional nonlinear systems with a center. The approach involves embedding nonlinear differential equations with polynomial terms into an infinite-dimensional linear system, which is then truncated to form a Carleman matrix. The block-matrix structure of the resulting Carleman matrices are utilized to obtain their spectrum. The calculation of eigenvectors, Jordan chains and Jordan basis of these Carleman matrices is presented. A simple example is then analyzed.

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带中心非线性系统的Carleman线性化：谱和Jordan基

本文介绍了用Carleman线性化方法分析二维非线性系统的行为。该方法包括将多项式项的非线性微分方程嵌入到一个无限维线性系统中，然后将其截断形成一个Carleman矩阵。利用得到的卡尔曼矩阵的分块矩阵结构得到其谱。给出了这些Carleman矩阵的特征向量、Jordan链和Jordan基的计算。然后分析了一个简单的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Sound and Vibration 工程技术-工程：机械

CiteScore

9.10

自引率

10.60%

发文量

551

审稿时长

69 days

期刊介绍： The Journal of Sound and Vibration (JSV) is an independent journal devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. There is an emphasis on fundamental work that has potential for practical application. JSV was founded and operates on the premise that the subject of sound and vibration requires a journal that publishes papers of a high technical standard across the various subdisciplines, thus facilitating awareness of techniques and discoveries in one area that may be applicable in others.