Toric steady states

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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


K_i \vec{c}^{\;y_j} - K_j \vec{c}^{\;y_i}

where i,j \in \mathcal{L}_k, k=1,\ldots, \ell (corresponding to the linkage classes).

References

  1. Gheorghe Craciun, Alicia Dickenstein, Anne Shiu, and Bernd Sturmfels, Toric dynamical systems, J. Symbolic Comput., 44(11):1551–1565, 2009