T. Ge et Ayt. Leung, CONSTRUCTION OF INVARIANT TORUS USING TOEPLITZ JACOBIAN MATRICES FASTFOURIER-TRANSFORM APPROACH, Nonlinear dynamics, 15(3), 1998, pp. 283-305
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 go
verning ODEs onto a set of partial differential equations (PDEs). A ne
w characteristic approach to determine the stability of resultant peri
odic surface is also developed. A system with two strongly coupled van
der Pol oscillators is taken as an illustrative example. The result s
hows that the Toeplitz Jacobian Matrix/Fast Fourier Transform (TJM/FFT
) approach introduced previously is accurate and efficient in this app
lication. The application of the method to normal multi-modes of nonli
near Euler beam is given in [1].