Model autocatalator

The autocatalator model is in many ways closely related to the FONT system, which has a single first-order exothennic reaction step obeying an Arrhenius temperature dependence and for which the role of the autocatalyst is taken by the temperature of the system. An extension of this is tlie Sal nikov model which supports tliennokinetic oscillations in combustion-like systems [48]. This has the fonn ... 

Gray, P. and Scott, S. K. (1986). A new model for oscillatory behaviour in closed systems the autocatalator. Ber. Bunsenges. Phys. Chem., 90,985-96. Hanusse, P. (1973). Etude des systemes dissipatifs chimiques a deux et trois especes intermediare. C. R. Acad. Sci., Paris, C277, 263., ... 

Parameter values exemplifying the 14 stationary-state responses for the reversible autocatalator model with Xo = -05 corresponding to Fig. 6.22... 

Balakotaiah, V. (1987). On the steady-state behaviour of the autocatalator model A + 2B 3B, B in a continuous-flow stirred-tank reactor Proc. R. Soc., A411, 193-206. 

The cubic autocatalator rate equations can be rigorously derived as a limiting form from a kinetic model involving only bimolecular steps. 

This example shows that mixed-mode oscillations, while arising from a torus attractor that bifurcates to a fractal torus, give rise to chaos via the familiar period-doubling cascade in which the period becomes infinite and the chaotic orbit consists of an infinite number of unstable periodic orbits. Mixedmode oscillations have been found experimentally in the Belousov-Zhabotin-skii (BZ) reaction 2.84 and other chemical oscillators and in electrochemical systems, as well. Studies of a three-variable autocatalator model have also provided insights into the relationship between period-doubling and mixedmode sequences. Whereas experiments on the peroxidase-oxidase reaction have not been carried out to determine whether the route to chaos exemplified by the DOP model occurs experimentally, the DOP simulations exhibit a route to chaos that is probably widespread in the realm of nonlinear systems and is, therefore, quite possible in the peroxidase reaction, as well. 

Gray, P. Scott, S. 1986. A New Model for Oscillatory Behaviour in Closed Systems The Autocatalator, Ber. Bunsenges. Phys. Chem. 90, 985-996. 

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