Reaction-diffusion wavefronts colliding with obstacles*

We developed an Obj-C computer simulation to study the propagation behavior of initially planar reaction-diffusion wavefronts colliding with convex obstacles in narrow two-dimensional channels. We used finite-difference numerical integration of the two-variable Tyson-Fife reduction for a set of three coupled differential equations, called the Oregonator model of the chemical Belousov-Zhabotinsky reaction.
The effect of obstacles on the wavefront shape is expressed, for example, by plotting the maximum wavefront delay versus time. After passing an obstacle, curvature dependent wavefront velocities restore the perturbed wavefront back to its initial planar shape and can be characterized by a power law. Recovery times are insensitive to obstacle concatenation or to the upstream obstacle shape but are sensitive to the downstream shape, with a vertical back side causing the longest disruption. Larger obstacles and larger obstacle width-to-length ratios, while keeping the area constant, produce larger wavefront delays and longer recovery times. Delays vary cyclically with obstacle orientations.