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The dynamical behavior of a higher-order cubic Ginzburg-Landau equation isfound to include a wide range of scenarios due to the interplay of higher-orderphysically relevant terms. We find that the competition between the third-orderdispersion and stimulated Raman scattering effects, gives rise to richdynamics: this extends from Poincar\'{e}-Bendixson--type scenarios, in thesense that bounded solutions may converge either to distinct equilibria viaorbital connections, or space-time periodic solutions, to the emergence ofalmost periodic and chaotic behavior. One of our main results is that thethird-order dispersion has a dominant role in the development of such complexdynamics, since it can be chiefly responsible (i.e., even in the absence of theother higher-order effects) for the existence of the periodic, quasi-periodicand chaotic spatiotemporal structures. Suitable low-dimensional phase spacediagnostics are devised and used to illustrate the different possibilities andidentify their respective parametric intervals over multiple parameters of themodel.

physical review. e

The dynamical playground of a higher-order cubic Ginzburg-Landau  equation: from orbital connections and limit cycles to invariant tori and the  onset of chaos