With a reaction-diffusion system, we consider the dispersing two-species
Lotka-Volterra model with a temporally periodic interruption of the interspecific
competitive relationship. We assume that the competition coefficient becomes a given
positive constant and zero by turns periodically in time. We investigate the condition
for the coexistence of two competing species in space, especially in the bistable case
for the population dynamics without dispersion. We could find that the spatial coexistence,
that is, the spatially mutual invasion of two competing species appears with two
opposite-directed travelling waves if a condition for the temporal interruption of the
interspecific relationship is satisfied. Further,
we give a suggested mathematical expression of the velocity of travelling waves.