Nonlinear oscillatory mixing in the generalized Landau scenario

R. Herrero, J. Farjas, F. Pi, G. Orriols
2018 Physical review. E  
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
more » ... 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.
doi:10.1103/physreve.97.052218 pmid:29906878 fatcat:pxuulejkxve73n7nog4kx2ye4q