In 1979, J. Schnakenberg introduced a system showing sustained oscillations for a simple model of glycolysis (a metabolic process that converts glucose to provide energy for metabolism), very similar to a system known as the "Brusselator" that consists of four reactions.
The reaction is trimolecular and involves autocatalysis: the reaction product is itself a catalyst for one step of the reaction. The reaction proceeds in three steps:
following the kinetic equations
,
.
Reference
[1] J. Schnakenberg, "Simple Chemical Reaction Systems with Limit Cycle Behaviour," Journal of Theoretical Biology, 81(3), 1979 pp. 389–400. doi: 10.1016/0022-5193(79)90042-0.
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