Information Exchange between Moving Particles and Defects

Pulse wave is one of the main careers of information and the effect of heterogeneity of the media in which it propagates is of great importance for the understanding of signaling processes in biological and chemical systems. A typical one dimensional heterogeneity is a spatially localized bump or dent, which creates associated defects in the media. To know the behaviors of pulse in such media is equivalent to study the collision process between the pulse and the defect. A variety of outputs are observed depending on the height and width of the bump such as rebound, pinning, oscillatory motion as well as penetration. A remarkable thing is that PDE dynamics can be reduced to finite dimensional one near a drift bifurcation and the defects become equilibrium points of the reduced ODEs. The basin of each equilibrium point and the switching among those basins explain all the outputs after collision with the defects. We employ a three-component reaction-diffusion system of one-activator-two-inhibitor type to illustrate these issues.