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Reducibility of Periodic Quasi-Periodic Systems

DOI: 10.4236/ijmnta.2014.31002    3,229 Downloads   4,987 Views  

ABSTRACT

In this work, the reducibility of quasi-periodic systems with strong parametric excitation is studied. We first applied a special case of Lyapunov-Perron (L-P) transformation for time periodic system known as the Lyapunov-Floquet (L-F) transformation to generate a dynamically equivalent system. Then, we used the quasi-periodicnear-identity transformation to reduce this dynamically equivalent system to a constant coefficient system by solving homological equations via harmonic balance. In this process, we obtained the reducibility/resonance conditions that needed to be satisfied to convert a quasi-periodic system in to a constant one. Assuming the reducibility is possible, we obtain the L-P transformation that can transform original quasi-periodic system into a system with constant coefficients. Two examples are presented that show the application of this approach.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Ezekiel, E. and Redkar, S. (2014) Reducibility of Periodic Quasi-Periodic Systems. International Journal of Modern Nonlinear Theory and Application, 3, 6-14. doi: 10.4236/ijmnta.2014.31002.

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