Canard phenomenon and localization of oscillations in the Belousov–Zhabotinsky reaction with global feedback

The occurrence of spatial domains of large amplitude oscillation on a background of small amplitude oscillation in a reaction–diffusion system is called localization. We study, analytically and numerically, the mechanism of localization in a model of the Belousov–Zhabotinsky reaction subject to global feedback. This behavior is found to arise from the canard phenomenon, in which a limit cycle suddenly undergoes a significant change in amplitude as a bifurcation parameter, in this case the feedback strength, is varied. In the system studied here, the oscillations arise via a supercritical Hopf bifurcation, but our analysis suggests that the same mechanism is relevant for systems undergoing a subcritical Hopf bifurcation. © 2003 American Institute of Physics. @DOI: 10.1063/1.1614752#