Spatiotemporal complexity in Ginzburg Landau equations for anisotropic systems - Zou, Yang, author; Oprea, Iuliana, advisor; Dangelmayr, Gerhard, advisor; Fassnacht, Steven, committee member; Shipman, Patrick, committee member (Colorado State University. Libraries, 2012)
Nematic electroconvection is a paradigm example of pattern formation in anisotropic extended systems, where spatiotemporal chaos can arise at the onset of electroconvection. This dissertation is devoted to characterize and identify the instability mechanism generating the spatiotemporal complexity in the numerical simulations of a system of Ginzburg Landau equations, used to study the weakly nonlinear stability of waves' amplitudes of nematic electroconvective patterns. In particular, the following results pertaining to spatiotemporal complexity are discussed. First, the simulated patterns are decomposed into central and noncentral spatial Fourier modes. The central modes form an invariant manifold, and the noncentral modes are transverse variables for this manifold. Simulations indicate that the bursts in the noncentral modes induce rapid switchings between a pair of symmetry-conjugated chaotic saddles in the central modes. Even though there are many degrees of freedom involved in these spatiotemporal chaotic patterns, a dimension reduction can be made by exploiting symmetries, leading to a small number of symmetry-adapted variables. A detailed investigation of the dynamics in the space of symmetry-adapted variables reveals that the spatiotemporal complexity is due to in-out intermittency caused by transverse instability of the invariant manifold. Second, in order to understand the instability mechanism causing the switching dynamics in terms of a low dimensional model, a normal form for a Hopf bifurcation with a broken translation variance posed in the space of the central modes is introduced. Theoretical issues relating to symmetries and invariant subspaces are studied. A series of complex phenomena, including symmetry breaking and increasing, period doubling, chaos, transient chaos, crisis-induced intermittency and in-out intermitteny, is observed when an imperfection parameter measuring the strength of the symmetry breaking is varied. In certain parameter regimes bursts with certain magnitudes trigger rapid switchings between a pair of chaotic saddles. A new type of dynamics, identified as a new type of intermittency, is also discussed. Conclusions and further development are presented at the end of the dissertation.