We investigate the transition to explosive dissipative solitons and the destruction of invariant tori in the complex cubic-quintic Ginzburg-Landau equation in the regime of anomalous linear dispersion as a function of the distance from linear onset. Using Poncaré sections, we sequentially find fixed points, quasiperiodicity (two incommesurate frequencies), frequency locking, two torus-doubling bifurcations (from a torus to a 2-fold torus and from a 2-fold torus to a 4-fold torus), the destruction of a 4-fold torus leading to non-explosive chaos, and finally explosive solitons. A narrow window, in which a 3-fold torus appears, is also observed inside the chaotic region.
Bibliographical noteFunding Information:
The authors acknowldge support from FONDECYT under project No. 1110360 and project No. 3110028 as well as from the Universidad de los Andes through FAI initiatives.
- cubic-quintic Ginzburg-Landau equation
- destruction of invariant tori
- explosive dissipative solitons