Topological study of multiple coexisting attractors in a nonlinear system

Multiple attractors in a new nonlinear dynamical system recently derived from the derivative nonlinear Schrodinger (DNLS) equation describing the Alfven turbulence in magnetized plasma are analyzed in the light of geometric characterization of orbit properties, which was originally introduced by Birman and Williams and later systematized by Gilmore, Mindlin, Letellier and others. We observe that the order in which periodic orbits appear is as predicted from their symbolic sequences by the universal sequence. The observed templates of increasing complexity are organized along a spiral (which is actually a two-dimensional homomorphic projection of the original attractor). Examples of explicit templates and their variation with respect to the parameter are exhibited.