Abstract
In this paper we investigate the transition from periodic solutions to spatiotemporal chaos in a system of four globally coupled Ginzburg Landau equations describing the dynamics of instabilities in the electroconvection of nematic liquid crystals, in the weakly nonlinear regime. If spatial variations are ignored, these equations reduce to the normal form for a Hopf bifurcation with \begin{document}$O(2) × O(2)$\end{document} symmetry. Both the amplitude system and the normal form are studied theoretically and numerically for values of the parameters including experimentally measured values of the nematic liquid crystal Merck I52. Coexistence of low dimensional and extensive spatiotemporal chaotic patterns, as well as a temporal period doubling route to spatiotemporal chaos, corresponding to a period doubling cascade towards a chaotic attractor in the normal form, and a kind of spatiotemporal intermittency that is characteristic for anisotropic systems are identified and characterized. A low-dimensional model for the intermittent dynamics is obtained by perturbing the eight-dimensional normal form by imperfection terms that break a continuous translation symmetry.
Highlights
In dissipative systems far from equilibrium, regular periodic states may undergo transitions to persistent spatiotemporal complex dynamics, a state known as spatiotemporal chaos (STC), which is unpredictable in both space and time and characterized by a fast decay of spatial and temporal correlations
In this paper we report on a study of the transition from periodic solutions to spatiotemporal chaos, via a temporal period doubling cascade, in a system of four globally coupled Ginzburg Landau equations describing the dynamics at the onset of a pattern forming instability in the electroconvection of nematic liquid crystals
We have presented the complex spatiotemporal dynamics shown by a system of four globally coupled complex Ginzburg Landau equations, which govern the dynamics of wave instabilities in two-dimensional anisotropic systems with two translational and two reflectional symmetries
Summary
In dissipative systems far from equilibrium, regular periodic states may undergo transitions to persistent spatiotemporal complex dynamics, a state known as spatiotemporal chaos (STC), which is unpredictable in both space and time and characterized by a fast decay of spatial and temporal correlations. In this paper we report on a study of the transition from periodic solutions to spatiotemporal chaos, via a temporal period doubling cascade, in a system of four globally coupled Ginzburg Landau equations describing the dynamics at the onset of a pattern forming instability in the electroconvection of nematic liquid crystals. In our Ginzburg-Landau analysis of the WEM equations near an oblique Hopf bifurcation, the complex amplitudes Aj are considered as slowly varying envelopes that modulate the travelling wave solutions of the linearized system at R = Rc. The dynamical equations for these envelopes follow from a weakly nonlinear, multiple scale analysis. Normal form ODE’s associated with Ginzburg Landau-type amplitude equations and the nonlinear maps used in coupled map lattices govern spatially uniform solutions of the corresponding spatiotemporal systems. In the subsections we present the results of the parameter study in the case of spatiotemporal complex dynamics of (7) induced by chaotic dynamics in the normal form (10)
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