Abstract
We investigate diffusion-induced instabilities of phase waves in one spatial dimension for a two-variable
model of the Belousov—Zhabotinsky reaction. We use as initial conditions small-amplitude phase waves
which exist in the parametric range between a canard point and a supercritical Hopf bifurcation point. Closer
to the canard point, the instability leads to initiation of trigger waves, usually at the zero flux boundary.
Such induced trigger waves reflect from the boundary, and when they collide, a new trigger wave emerges
at the location of the collision. When the parameters are chosen nearer to the Hopf point, the phase waves
lose their regular pattern and become uncorrelated. Very close to the Hopf point, diffusion alters the phase
wave profile into small-amplitude synchronized bulk oscillations. Different types of spatiotemporal behavior
are observed when the wavelength of the phase waves, the overall size of the system, or the diffusion coefficients
are changed. Comparison of the behavior near a canard and near a subcritical Hopf bifurcation shows that
in the former case trigger waves can be initiated at all points of the excitable medium, whereas in the latter
case trigger waves are generated only at the boundary.