Unsteady fronts in an autocatalytic system

Travelling waves in a model for autocatalytic reactions have, for some para meter regimes, been suggested to have oscillatory instabilities. These inst abilities are confirmed by various methods, including linear-stability anal ysis (exploiting Evens's function) and direct numerical simulations. The fr ont instability sets in when the order of the reaction, m, exceeds some thr eshold, m(c)(tau): that depends on the inverse of the Lewis number, tau. Th e stability boundary, m = m(c)(tau), is found numerically for m order one. In the limit m much greater than 1 (in which the system becomes similar to combustion systems with Arrhenius kinetics), the method of matched asymptot ic expansions is employed to find the asymptotic front speed and show that m(c) similar to (tau-1)(-1) as tau --> 1. Just beyond the stability boundar y, the unstable rocking of the front saturates supercritically. If the orde r is increased still further, period-doubling bifurcations occur, and for s mall tau there is a transition to chaos through intermittency after the dis appearance of a period-4 orbit.