Toric steady states
A mass action system is said to have toric steady states if the steady state ideal is generated by binomials.
Complex balanced systems
It was shown by Craciun et al.[1] that every complex balanced mass action system has toric steady states. In particular, we have that the steady state ideal is generated by the binomials
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where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i,j \in \mathcal{L}_k, k=1,\ldots, \ell} (corresponding to the linkage classes).
References
- ↑ Gheorghe Craciun, Alicia Dickenstein, Anne Shiu, and Bernd Sturmfels, Toric dynamical systems, J. Symbolic Comput., 44(11):1551–1565, 2009