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Polynomial dynamical systems (i.e. dynamical systems with polynomial righthand side) are ubiquitous in applications, especially as models of reactionnetworks and interaction networks. The properties of general polynomialdynamical systems can be very difficult to analyze, due to nonlinearity,bifurcations, and the possibility for chaotic dynamics. On the other hand,toric dynamical systems are polynomial dynamical systems that appear naturallyas models of reaction networks, and have very robust and stable properties. Adisguised toric dynamical system is a polynomial dynamical system generated bya reaction network $\mathcal N$ and some choice of positive parameters, suchthat (even though it may not be toric with respect to $\mathcal N$) it has atoric realization with respect to some network $\mathcal N'$. Disguised toricdynamical systems enjoy all the robust stability properties of toric dynamicalsystems. In this paper, we study a larger set of dynamical systems where therate constants are allowed to take both positive and negative values. Moreprecisely, we analyze the $\mathbb{R}$-disguised toric locus of a reactionnetwork $\mathcal N$, i.e., the subset in the space rate constants (positive ornegative) of $\mathcal N$ for which the corresponding polynomial dynamicalsystem is disguised toric. We focus especially on finding a lower bound on thedimension of the $\mathbb{R}$-disguised toric locus.

A Lower Bound on the Dimension of the $\mathbb{R}$-Disguised Toric Locus of a Reaction Network