Abstract
The temporal evolution of a resonant sideband system, obtained from a nonlinear evolution equation of Ginzburg-Landau type, is studied. In the phase space of an associated three-dimensional dynamical system, a non-trivial attractor is discovered within certain parameter ranges. The present attractor differs from well-known non-trivial attractors of either Lorenz or Silnikov type in that it does not result from homoclinic bifurcation, but rather relates to the break-down of heteroclinic cycles and the creation of global non-planar limit cycles, and results from the motion of stable and unstable manifolds of three global limit cycles. It shares however some common features of bifurcating sequences: a stable non-planar limit cycle → an aperiodic attractor → a pair of spiral sinks, which in an asymptotic state correspond respectively to periodic, chaotic, or steady modulation of the sideband wave system in physical space.
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