A period doubling route to spatiotemporal chaos in a system of Ginzburg-Landau equations for nematic electroconvection

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 O(2) × O(2) 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.

Electric-field-induced avalanches and glassiness of mobile ferroelastic twin domains in cryogenic SrTiO3

“…As indicated by the arrows in Fig. 4(a), the main effect is period doubling of the sequence of thin walls [25][26][27][28][29][30][31]. Applying the same procedure as before, we tracked the birefringence as a function of time while cycling the electric field and constructed the jerk spectra (see details in the Supplemental Material [32]).…”