title: Dynamical playground of a higher-order cubic Ginzburg-Landau equation: From orbital connections and limit cycles to invariant tori and the onset of chaos.
abstract: The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order dispersion and stimulated Raman scattering effects gives rise to rich dynamics: this extends from Poincaré-Bendixson-type scenarios, in the sense that bounded solutions may converge either to distinct equilibria via orbital connections or to space-time periodic solutions, to the emergence of almost periodic and chaotic behavior. One of our main results is that third-order dispersion has a dominant role in the development of such complex dynamics, since it can be chiefly responsible (even in the absence of other higher-order effects) for the existence of periodic, quasiperiodic, and chaotic spatiotemporal structures. Suitable low-dimensional phase-space diagnostics are devised and used to illustrate the different possibilities and identify their respective parametric intervals over multiple parameters of the model.
authors: Laboratoire d' Acoustique de l' Université du Maine, Avenue O. Messiaen, 72085 Le Mans, France.
authors: V
authors: V
authors: Achilleos
authors: Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors: A R
authors: AR
authors: Bishop
authors: Department of Mathematics, University of the Aegean, Karlovassi, 83200 Samos, Greece.
authors: S
authors: S
authors: Diamantidis
authors: Department of Physics, University of Athens, Panepistimiopolis, Zografos, 15784 Athens, Greece.
authors: D J
authors: DJ
authors: Frantzeskakis
authors: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece.
authors: T P
authors: TP
authors: Horikis
authors: Department of Mathematics, University of the Aegean, Karlovassi, 83200 Samos, Greece.
authors: N I
authors: NI
authors: Karachalios
authors: Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.|Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
authors: P G
authors: PG
authors: Kevrekidis