WOB Examples

Isothermal Reaction

Original source is K. D. Williamowski, O. E. Rössler (1979), quoted in: C. B. Smith, B. Kuszta, G. Lyberatos, J. E. Bailey: Period doubling and complex dynamics in an isothermal chemical reaction system. Chem. Eng. Sci. 38 (1983) 425-430.

Four parameter values of period doubling are

$\begin{displaymath}\lambda_1&=10.5710\cr\end{displaymath}$

$\begin{displaymath}\lambda_2&=10.1465\cr\end{displaymath}$

$\begin{displaymath}\lambda_3&=10.0912\cr\end{displaymath}$

$\begin{displaymath}\lambda_4&=10.0808.\cr\end{displaymath}$

The expected accumulation point is $\lambda_\infty =10.078$ .

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.

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