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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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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.

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Ricardo Lopez-Ruiz. 2003-09-04. Symmetry induced Dynamics in four-dimensional Models deriving from the van der Pol Equation. https://doi.org/10.1016/j.chaos.2003.09.033

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