Computation and continuation of quasiperiodic solutions

Schilder, Frank; Vogt, Werner GND

We consider periodically forces ODEs which exhibit quasiperiodic oscillations. These oscillations are investigated by an approximation and continuation of the associated invariant torus with respect to free system parameters. For the invariant torus we derive an uncomplicated invariance equation whereby we do not require the system to be partitioned or an a-priori-coordinate transformation to be applied. This equation is solved by semidiscretisation methods where Fourier-Galerkin methods especially in the case of periodically forced "weakly nonlinear" ODEs lead to low dimensional autonomous systems which can be treated by standard algorithms. Also in the general use it turns out that this approach allows an efficient computation and continuation of quasiperiodic solutions. A number of problems has been analysed successfully and an example is given in this paper.

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Schilder, Frank / Vogt, Werner: Computation and continuation of quasiperiodic solutions. 2001.

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