In–Out Intermittency with Nested Subspaces in a System of Globally Coupled, Complex Ginzburg–Landau Equations

Abstract

Chaos and intermittency are studied for the system of globally coupled, complex Ginzburg–Landau equations governing the dynamics of extended, two-dimensional anisotropic systems near an oscillatory (Hopf) instability of a basic state with two pairs of counterpropagating, oblique traveling waves. Parameters are chosen such that the underlying normal form, which governs the dynamics of the spatially constant modes, has two symmetry-conjugated chaotic attractors. Two main states residing in nested invariant subspaces are identified, a state referred to as Spatial Intermittency ([Formula: see text]) and a state referred to as Spatial Persistence ([Formula: see text]). The [Formula: see text]-state consists of laminar phases where the dynamics is close to a normal form attractor, without spatial variation, and switching phases with spatiotemporal bursts during which the system switches from one normal form attractor to the conjugated normal form attractor. The [Formula: see text]-state also consists of two symmetry-conjugated states, with complex spatiotemporal dynamics, that reside in higher dimensional invariant subspaces whose intersection forms the 8D space of the spatially constant modes. We characterize the repeated appearance of these states as (generalized) in–out intermittency. The statistics of the lengths of the laminar phases is studied using an appropriate Poincaré map. Since the Ginzburg–Landau system studied in this paper can be derived from the governing equations for electroconvection in nematic liquid crystals, the occurrence of in–out intermittency may be of interest in understanding spatiotemporally complex dynamics in nematic electroconvection.