DIFFUSION-INDUCED INSTABILITIES NEAR A CANARD

We investigate diffusion-induced instabilities of phase waves in one s patial dimension for a two-variable model of the Belousov-Zhabotinsky reaction. We use as initial conditions small-amplitude phase waves whi ch exist in the parametric range between a canard point and a supercri tical Hopf bifurcation point. Closer to the canard point, the instabil ity leads to initiation of trigger waves, usually at the zero flux bou ndary. Such induced trigger waves reflect from the boundary, and when they collide, a new trigger wave emerges at the location of the collis ion. When the parameters are chosen nearer to the Hopf point, the phas e 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 spatiote mporal behavior are observed when the wavelength of the phase waves, t he overall size of the system, or the diffusion coefficients are chang ed. Comparison of the behavior near a canard and near a subcritical Ho pf bifurcation shows that in the former case trigger waves can be init iated at all points of the excitable medium, whereas in the latter cas e trigger waves are generated only at the boundary.