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Symmetry induced Dynamics in four-dimensional Models deriving from the van der Pol Equation | Ricardo Lopez-Ruiz
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4 Sep 2003 | Subject: | Chaotic Dynamics; Pattern Formation and Solitons | nlin.CD nlin.PS | Abstract: | Different models of self-excited oscillators which are four-dimensional extensions of the van der Pol system are reported. Their symmetries are analyzed. Three of them were introduced to model the release of vortices behind circular cylinders with a possible transition from a symmetric to an antisymmetric Benard-von Karman vortex street. The fourth reported self-excited oscillator is a new model which implements the breaking of the inversion symmetry. It presents the phenomenon of second harmonic generation in a natural way. The parallelism with second harmonic generation in nonlinear optics is discussed. There is also a small region in the parameter space where the dynamics of this system is quasiperiodic or chaotic. | Source: | arXiv, nlin.CD/0309013 | Services: | Forum | Review | PDF | Favorites |
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