Dynamical Systems
2nd order models - exercises
Exercise 1
\[
\begin{cases}
\dot{x}_1= -2 x_1 + 4 x_2 \qquad \mbox{(metabolite)}\\
\dot{x}_2= 2 x_2 \qquad \mbox{(enzyme)}
\end{cases}
\]
- Does the enzyme promote the production or the consumption of the metabolite?
- Does the metabolite impact the enzyme?
- What type phase space do we have?
Exercise 2
\[
\begin{cases}
\dot{x}_1= 2 x_1 - 4 x_2 \qquad \mbox{(metabolite)}\\
\dot{x}_2= 1 x_2 \qquad \mbox{(enzyme)}
\end{cases}
\]
- Does the enzyme promote the production or the consumption of the metabolite?
- Does the metabolite impact the enzyme?
- What type phase space do we have?
Exercise 3
\[
\begin{cases}
\dot{x}_1= -2 x_1 + 6 x_2 \qquad \mbox{(metabolite)}\\
\dot{x}_2= -4 x_1 + 2 x_2 \qquad \mbox{(enzyme)}
\end{cases}
\]
- Does the enzyme promote the production or the consumption of the metabolite?
- Does the metabolite impact the enzyme?
- What type phase space do we have?
