The behaviour of a model branched-chain reaction with radical termination is investigated for a well-stirred flow reactor. The termination step is assumed to be exothermic and the chain-branching or autocatalysis has an Arrhenius temperature dependence. Under adiabatic conditions, ignition and extinction phenomena are exhibited in the form of a hysteresis loop. For a non-adiabatic reactor more complex stationary state bifurcation diagrams, including isola responses, are found. Dynamic instabilities also arise, with simple periodic oscillations emerging from Hopf bifurcations. These periodic solutions may undergo secondary bifurcations, typically through period-doubling: a full cascade to chaotic responses is found. A comparison of this model with simpler schemes and its implications for various combustion reactions are discussed.
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Liu et al. (1993) studied this question.
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