An Organizing Center for Tracefiring of Pulses in the Oregonator
by
Jens Rademacher
University of Minnesota

Tracefiring, the periodic creation of secondary trailing waves, has been observed in several models near an instability of a primary travelling pulse. In some cases a heteroclinic cycle between two equilibria ('T-point') in the pulse's travelling wave ODE forms an organizing center in terms of existence of constituents in spatial dynamics and their PDE-stability. We consider this phenomenon in the Oregonator model for the light sensitive BZ-reaction, where there is no relevant second equilibrium, but a periodic orbit. We rigorously show how a heteroclinic cycle with a periodic orbit yields an analogous organizing center. A biproduct is an existence theory for homoclinic orbits near heteroclinic chains with periodic orbits. Simulations, numerical pathfollowing and spectral computations corroborate the idea of this organizing center for the Oregonator.

We further comment on another point of view, where tracefiring is a defect that separates a spatio-temporally homogeneous region from a spatio-temporally periodic one.

Date received: October 27, 2003