Structural instability and sustained oscillations in an extended Brusselator model

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Abstract
When all reactions in the "Brusselator" kinetic scheme are allowed to be reversible one can demonstrate, by analyzing the focal values, that, for a range of rate constants, a unique limit cycle is created from a multiple focus. A simple modification of the kinetic scheme leads to a model that has two saddle nodes in addition to the well-known unstable focus and a stable limit cycle. In the modified system, for some parameter values, the limit cycle disappears after evolving into a saddle-node connection. For some initial conditions the modified system has unbounded solutions that describe a possible explosion. The analysis that yields these results is based on a general, constructive procedure, which can be applied to higher order physical and chemical systems.
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