Here we propose mechanisms for suppressing non-steady-state motions-propaga
ting pulses, spiral waves, spiral-wave chaos-in excitable media. Our approa
ch is based on two points: (1) excitable media are multistable; and (2) tra
veling waves in excitable media can be separated into fast and slow motions
, which can be considered independently. We show that weak impulses can be
used to change the values of the slow variable at the front and back of a t
raveling wave, which leads to wave front and wave back velocities that are
different: from each other. This effect can destabilize the traveling wave,
resulting in a transition to the rest state. [S1063-651X(99)00206-8].