Nonlinear oscillatory mixing in the generalized Landau scenario
PublisherAmerican Institute of Physics (AIP)
Rights accessOpen Access
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.
CitationHerrero, R., Farjas, J., Pi, F., Orriols, G. Nonlinear oscillatory mixing in the generalized Landau scenario. "Physical review E", 31 Maig 2018, vol. 97, núm. 5, p. 052218-1-052218-14.
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