Construction of Invariant Torus Using Toeplitz Jacobian Matrices/Fast Fourier Transform Approach

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

12 Scopus Citations
View graph of relations

Author(s)

  • T. Ge
  • A. Y T Leung

Detail(s)

Original languageEnglish
Pages (from-to)283-305
Journal / PublicationNonlinear Dynamics
Volume15
Issue number3
Publication statusPublished - 1998
Externally publishedYes

Abstract

The invariant torus is a very important case in the study of nonlinear autonomous systems governed by ordinary differential equations (ODEs). In this paper a new numerical method is provided to approximate the multiperiodic surface formed by an invariant torus by embedding the governing ODEs onto a set of partial differential equations (PDEs). A new characteristic approach to determine the stability of resultant periodic surface is also developed. A system with two strongly coupled van der Pol oscillators is taken as an illustrative example. The result shows that the Toeplitz Jacobian Matrix/Fast Fourier Transform (TJM/FFT) approach introduced previously is accurate and efficient in this application. The application of the method to normal multi-modes of nonlinear Euler beam is given in [1].

Research Area(s)

  • Fast fourier transform, Invariant torus, Toeplitz Jacobian matrix, Van der Pol oscillator

Citation Format(s)

Construction of Invariant Torus Using Toeplitz Jacobian Matrices/Fast Fourier Transform Approach. / Ge, T.; Leung, A. Y T.

In: Nonlinear Dynamics, Vol. 15, No. 3, 1998, p. 283-305.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review