We investigate the possibility of projecting low dimensional chaos from
spatiotemporal dynamics of a model for a kind of plastic instability observed
under constant strain rate deformation conditions. We first discuss the
relationship between the spatiotemporal patterns of the model reflected in the
nature of dislocation bands and the nature of stress serrations. We show that
at low applied strain rates, there is a one-to-one correspondence with the
randomly nucleated isolated bursts of mobile dislocation density and the stress
drops. We then show that the model equations are spatiotemporally chaotic by
demonstrating the number of positive Lyapunov exponents and Lyapunov dimension
scale with the system size at low and high strain rates. Using a modified
algorithm for calculating correlation dimension density, we show that the
stress-strain signals at low applied strain rates corresponding to spatially
uncorrelated dislocation bands exhibit features of low dimensional chaos. This
is made quantitative by demonstrating that the model equations can be
approximately reduced to space independent model equations for the average
dislocation densities, which is known to be low-dimensionally chaotic. However,
the scaling regime for the correlation dimension shrinks with increasing
applied strain rate due to increasing propensity for propagation of the
dislocation bands.Comment: 9 pages, 19 figure
