Many pattern forming systems in both physics and biology exhibit complex behavior in space and time termed spatiotemporal chaos. Whereas the analysis of dynamical quantities such as Lyapunov exponents has provided insight into low-dimensional systems, the application of these techniques to high-dimensional systems has been limited, partly due to the computational expense. I will discuss two large-scale computational studies in which my collaborators and I analyzed the detailed space-time evolution of the dynamical degrees of freedom (characterized by the Lyapunov vectors and exponents) in two pattern-forming, spatiotemporal chaotic systems, Rayleigh-Benard convection and fibrillating heart tissue. In both of these systems we found that the mechanism for the generation of chaotic behavior is spatially and temporally localized to particular types of events, such as the creation and annihilation of defects. This knowledge of the particular areas sensitive to stimuli may lead to new ways to control spatiotemporal systems and, in particular, may result in a new method for defibrillation less extreme than current techniques.
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