Nt1310 Unit 1 Study Guide

Let $x(t)=(x_1(t),\ldot,x_n(t))$ be the concentration of the species on the instant $t$. Consider the representation of a chemical reaction network in terms of differential equations,

\begin{equation}
\frac{dx_i}{xt} = f_i(x), \:\:i=1,\ldot\n
\end{equation}

The point of interest is to determine if the system admits multiple positive steady states. Therefore, figure if the following equation admits more than one strictly positive solution,

\begin{equation} f_i(x)=0, \:\:i=1,\ldot\n.
\end{equation}

Consider the matrices $A$ and $V$, and the parameters $\kappa$, that correspond to the constant rates of the reactions, such that

$$f(x) = A(\kappa\circ x^V).$$

The method implemented uses this representation of the polynomial map $f$ and infers