Construction of invariant torus using Toeplitz Jacobian Matrices/Fast Fourier Transform approach
Author(s)
Author(s)
Ge, T.
Date Issued
1998
Publisher
Springer
Journal
Nonlinear Dynamics
Volume
15
Issue
3
Start page
283
End page
305
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 multi-periodic 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].
SFU Affiliated Publication
No
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