Autocatalytic reactions are chemical reactions in which at least one of the products is also a reactant. This "feed-back loop" yields a system of nonlinear polynomial equations. A famous example is called the Brusselator [1], [2]. Although the equations describing the classic Brusselator are trivial, the basic idea generalizes to more interesting situations [1], such as

        a + x1²*y1 - b*x1 - x1 + dx (x2 - x1),
        b*x1 - x1²*y1 + dy (y2 - y1),
        a + x2²*y2 - b*x2 - x2 + dx (x1 - x2),
        b*x2 - x2²*y2 + dy (y1 - y2)

We will examine the systems of equations that result from two- and three-dimensional configurations of interacting Brusselators. We have up to eight equations in eight variables and up to twelve parameters. We find that all are solvable with Dixon resultant methods. We will describe how various implementations of Groebner Bases fail on all but the simplest cases. We will show other examples of autocatalytic reactions.

[1] http://en.wikipedia.org/wiki/Autocatalytic_reaction
[2] Shaun Ault, http://fordham.academia.edu/ShaunAult/Papers/83373/Dynamics-of-the-Brusselator