Isothermal Reaction

exd13
Variables and parameter:

yi(t): chemical species, i=1,2,3

$\lambda$: reaction rate

\begin{displaymath}\dot y_1 & = y_1 (30 - 0.25y_1 - y_2 - y_3) + 0.001y^2_2 + 0.1 \cr\end{displaymath}


\begin{displaymath}\dot y_2 & = y_2 (y_1 - 0.001y_2 - \lambda ) + 0.1 \cr\end{displaymath}


\begin{displaymath}\dot y_3 & = y_3 (16.5 - y_1 - 0.5y_3) + 0.1 \ \cr\end{displaymath}



There is a Hopf bifurcation at $\lambda_0=12.1435$, and a sequence of period doubling bifurcations.

Comments

Figure 1
Bifurcation diagram, y1(0) versus $\lambda$.

Figure 2
Isothermal reaction, periodic orbit, $\lambda=10.55$, projection to (y1,y2) plane.

Figure 3
Isothermal reaction, periodic orbit, $\lambda=10.13$, projection to (y1,y2) plane.

Figure 4
Isothermal reaction, chaotic orbit, $\lambda=10$, projection to (y1,y2) plane.

Postscript-Files for better printing results:

This Example
Figure 1
Figure 2
Figure 3
Figure 4