Localized patterns in driven dissipative systems
Yi-Ping Ma
Applied Mathematics, University of Colorado Boulder
Date and time:
Tuesday, October 15, 2013 - 4:30pm
Location:
ECOT 226
Abstract:
This talk provides an overview of some recent development in the study of spatially localized states in pattern forming systems. These localized states are observed in physical systems ranging from ferrofluids to vibrated granular media, and often result from bistability between a spatially homogeneous state and a spatially periodic state. I will emphasize insights gained from the study of three paradigmatic pattern forming PDEs, namely the quadratic-cubic Swift-Hohenberg equation, the harmonically (or 1:1) forced complex Ginzburg-Landau equation, and the Brusselator model. In each case it is shown how the nature of the bistability determines the spatial bifurcation structures and temporal dynamics of spatially localized states.