Symbol dynamic maps of spatial-temporal chaotic vibrations in a string of impact oscillators

Spatially complex, temporally chaotic dynamics of N-coupled impact oscillators connected by a string are studied experimentally using a discrete measure of the motion for each of the masses. For N = 8, a binary assignment of symbols, corresponding to whether or not the masses impact an amplitude constraint, is used to code the spatial pattern as a binary number and to store its change in time in a computer. A spatial pattern return map is then used to observe the change in spatial patterns with time. Bifurcations in spatial impact patterns are observed in this experiment. An entropy measure is also used to characterize the dynamics. Numerical simulation shows behavior similar to the experimental system.