Forced reaction in a CSTR. A comparison between the full system and the reduced model

In this paper, a periodically forced Gray-Yang thermokinetic reaction in a CSTR is considered. Here, we compare the dynamical behavior of the full four-variable system with its two-variable counterpart. The latter model was derived by examining the reaction in the 'short' time scale. We show that, for high flow rates as well as ambient temperatures, the reduced system provides an excellent approximation of the exact solutions (for both the autonomous and forced reactions). These similarities include the locations of the Hopf and saddle-node bifurcation points, the routes from periodic to chaotic behaviour, and in some cases even the locations of the windows of periodic behaviour in the region of chaos. However, in some parameter regions (particularly at very low flow rates), the system of four equations predicts extra bifurcation behaviours in a narrow 'boundary layer', that are absent in the two-variable model. Nevertheless, the overall dynamical behaviours observed from these schemes are identical in many instances.