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arXiv · 1711.06536

Nonlinear oscillatory mixing in the generalized Landau scenario

R. Herrero·J. Farjas·F. Pi·G. Orriols
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Abstract

We present a set of phase-space portraits illustrating the extraordinary oscillatory possibilities of the dynamical systems through the so-called generalized Landau scenario. In its simplest form the scenario develops in N dimensions around a saddle-node pair of fixed points experiencing successive Hopf bifurcations up to exhausting their stable manifolds and generating N-1 different limit cycles. The oscillation modes associated with these cycles extend over a wide phase-space region by mixing ones within the others and by affecting both the transient trajectories and the periodic orbits themselves. A mathematical theory covering the mode-mixing mechanisms is lacking, and our aim is to provide an overview of their main qualitative features in order to stimulate research on it.

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R. Herrero, J. Farjas, F. Pi, G. Orriols. 2017-11-17. Nonlinear oscillatory mixing in the generalized Landau scenario. https://doi.org/10.1103/physreve.97.052218

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