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].
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Ge, T., Leung, A.Y.T. Construction of Invariant Torus Using Toeplitz Jacobian Matrices/Fast Fourier Transform Approach. Nonlinear Dynamics 15, 283–305 (1998). https://doi.org/10.1023/A:1008246602555
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DOI: https://doi.org/10.1023/A:1008246602555