Spatiotemporal control of excitable media is of paramount importance in the
development of new applications, ranging from biology to physics. To this end
we identify and describe a qualitative property of excitable media that enables
us to generate a sequence of traveling pulses of any desired length, using a
one-time initial stimulus. The wave trains are produced by a transient
pacemaker generated by a one-time suitably tailored spatially localized finite
amplitude stimulus, and belong to a family of fast pulse trains. A second
family, of slow pulse trains, is also present. The latter are created through a
clumping instability of a traveling wave state (in an excitable regime) and are
inaccessible to single localized stimuli of the type we use. The results
indicate that the presence of a large multiplicity of stable, accessible,
multi-pulse states is a general property of simple models of excitable media.Comment: 6 pages, 6 figure