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<p>The concept of spectral submanifolds, a powerful method of model order reduction of nonlinear systems, is extended to time delay systems that have infinite dimensional phase space representation. The proposed sun-star calculus based algorithm results in system reduction to manifolds which are constructed corresponding to either a real eigenvalue or to a pair of complex conjugate eigenvalues of the linearized system. Furthermore, it allows an improved approximation of self-excited oscillations exactly at the parameter point of interest, which could be further away from the corresponding Hopf bifurcation point. The paper includes case studies that demonstrate the capabilities of the algorithm.</p>

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Spectral submanifolds in time delay systems

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年1月27日

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  • Bence Szaksz,
  • Gábor Orosz,
  • Gábor Stepan

摘要

The concept of spectral submanifolds, a powerful method of model order reduction of nonlinear systems, is extended to time delay systems that have infinite dimensional phase space representation. The proposed sun-star calculus based algorithm results in system reduction to manifolds which are constructed corresponding to either a real eigenvalue or to a pair of complex conjugate eigenvalues of the linearized system. Furthermore, it allows an improved approximation of self-excited oscillations exactly at the parameter point of interest, which could be further away from the corresponding Hopf bifurcation point. The paper includes case studies that demonstrate the capabilities of the algorithm.