This observation is of particular interest because in real physical systems symmetries are rarely exact and symmetry-breaking imperfections must be assumed to be present. This dissertation shows that forced symmetry-breaking can lead to periodic or irregular bursts of very large dynamic range. The results are applied to relevant hydrodynamical systems. First, a model of large aspect-ratio binary fluid convection which considers the competition between two nearly degenerate modes of opposite parity is studied. For open parameter regimes, it is shown that periodic or irregular bursting with very large dynamic range may occur close to threshold.
Global connections involving finite amplitude states are also present.
The intricate sequence of bifurcations that take place is described in several cases, and the robustness of the results to small higher order terms in the amplitude equations is demonstrated. The forcing breaks the continuous normal form symmetry of the amplitude equations. Windows in which stable periodic solutions exist are also found and are associated with the traversal in parameter space through Arnol'd tongues. In addition, it is shown that bursts related to those found in the model of large aspect-ratio binary fluid convection may arise due to the forcing. Here the onset of bursting can be via an interior crisis or Type I intermittency.