Chaotic Pulses for Discrete Reaction Diffusion Systems

Existence and dynamics of chaotic pulses on 1D lattice are discussed. Traveling pulses arise typically in reaction diffusion systems like the FitzHugh-Nagumo equations. Such pulses annihilate when they collide each other. A new type of traveling pulse has been found recently in many systems where pulses bounce off like elastic balls. We consider the behavior of such a localized pattern on 1D lattice, i.e., an infinite system of ODEs with nearest interaction of diffusive type. Besides the usual standing and traveling pulses, a new type of localized pattern, which moves chaotically on a lattice, was found numerically. Employing the strength of diffusive interaction as a bifurcation parameter, there appear route from standing pulse to chaotic pulse; intermittent type I and type III. If two chaotic pulses collide with an appropriate timing, it forms a periodic oscillating pulse called molecule. Interaction among many chaotic pulses is also studied numerically.