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 journal › peer-review
Author(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 283-305 |
| Journal / Publication | Nonlinear Dynamics |
| Volume | 15 |
| Issue number | 3 |
| Publication status | Published - 1998 |
| Externally published | Yes |
Link(s)
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 journal › peer-review
