SIDE-BAND EVOLUTION OF A COMPLEX GINZBURG-LANDAU EQUATION - A 3-DIMENSIONAL DYNAMICAL SYSTEM AND ITS RESULTING NEW APERIODIC ATTRACTOR

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