Further reduction of nonzero terms in realizable chemical systems

Determine whether the number of nonzero terms in the polynomial ODE representations of the nine realizable geometric equivalence classes can be reduced below the 8–10 nonzero terms achieved by the constructed examples.

Background

The paper classifies strongly non-hyperbolic equilibria of planar second-order chemical reaction systems and shows that nine of Lyagina’s sixteen geometric equivalence classes can be realized when the equilibrium is positive. The authors computationally construct examples for each realizable class having 8–10 nonzero polynomial terms, after imposing the restriction that the coefficient a_{0,2} vanishes.

The discussion observes that additional coefficients may potentially be eliminated. Because a single chemical reaction can generate nonzero terms in both ODE components simultaneously, reducing the number of chemical reactions is a related but distinct objective. The unresolved question specifically concerns whether the number of nonzero terms in the ODE representation can be reduced further.