Using rigorous mathematical analysis, the nature of the thermo-kinetic steady states is investigated, and particular attention is paid to the existence of stable limit cycles originating from supercritical Hopf bifurcations. These oscillations representing the 'cool flames' disappear at the low temperature limit via limit cycle-saddle point bifurcations. The origin of 'two-stage' ignitions is traced to these bifurcations; the computed trajectories exhibit 'shoulders' characteristic of such ignitions. The system shows hysteresis in the transitions between oscillatory and non-oscillatory steady states.
|Number of pages||20|
|Journal||Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences|
|Publication status||Published - 8 Sep 1983|