  We analyze the effects of spatially extended periodic forcing on the dynamics
of one-dimensional excitation waves. Entrainment of unstable primary waves has
been studied numerically for different amplitudes and frequencies of additional
sub-threshold stimuli. We determined entrainment regimes under which excitation
blocks were transformed into consistent 1:1 responses. These responses were
spatially homogeneous and synchronized in the entire excitable medium. Compared
to primary pulses, pulses entrained by secondary stimulations were stable at
considerably shorter periods which decreased at higher amplitudes and greater
number of secondary stimuli. Our results suggest a practical methodology for
stabilization of excitation in reaction-diffusion media with regions of reduced
excitability.
