CONSTRUCTION OF INVARIANT TORUS USING TOEPLITZ JACOBIAN MATRICES FASTFOURIER-TRANSFORM APPROACH

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].