Explosion of limit cycles and chaotic waves in a simple nonlinear chemicalsystem - art. no. 026209

We consider a simple model of an autocatalytic chemical reaction where a li mit cycle rapidly increases to infinite period and amplitude, and disappear s under variation of a parameter. We show that this bifurcation can be unde rstood from seeing the system as a singular perturbation problem, and we fi nd the bifurcation point by an asymptotic analysis. Scaling laws for period and amplitude are derived. The unphysical bifurcation to infinity disappea rs under generic modifications of the model, and for a simple example we sh ow is replaced by a canard explosion, that is, a narrow parameter interval with an explosive growth of the amplitude. The bifurcation to infinity intr oduces a strong sensitivity that may result in chaotic dynamics if diffusio n is added. We show that this behavior persists even if the kinetics is mod ified to preclude the bifurcation to infinity.