Nonlinear oscillatory mixing in the generalized Landau scenario release_zs4c55zaw5dtjcgpjivwyd2qmi

by R. Herrero, J. Farjas, F. Pi, G. Orriols

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2021  

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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Type  article
Stage   accepted
Date   2021-02-26
Version   v3
Language   en ?
arXiv  1711.06536v3
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