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Stoichiometric Subspace

The stoichiometric subspace of a reaction network is the real vector space spanned by its reaction vectors y^'-y (Boros and Hofbauer 2020). Thus

S=spanR{y^'-y:y->y^'}.

A mass-action system has its vector field in S, so a trajectory starting at x^0 remains in x^0+S. Its positive stoichiometric compatibility class is

P=(x^0+S) intersection R_(>0)^d.

For the two-species network A⇄B, S is spanned by (-1,1), and every positive compatibility class is an open line segment x_1+x_2=c with c>0. The total concentration is conserved.

See also

Mass-Action System, Reaction Network, Vector Space Span, Weakly Reversible Reaction Network

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References

Boros, B. and Hofbauer, J. "Permanence of Weakly Reversible Mass-Action Systems with a Single Linkage Class." SIAM J. Appl. Dyn. Syst. 19, 352-365, 2020. https://doi.org/10.1137/19M1248431.

Cite this as:

Weisstein, Eric W. "Stoichiometric Subspace." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StoichiometricSubspace.html

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