Chemical oscillators that behave like a double pendulum
Before considering a double pendulum, let us consider a simple pendulum, which is modeled by

$$\ddot \theta + \frac{g}{\ell} \sin (\theta) = 0$$

Choosing units that make $\frac{g}{\ell} =1$, we have

$$\ddot \theta + \sin (\theta) = 0$$

Let $x_1 := \theta$ and $x_2 := \dot \theta$. Hence, the 2nd order ODE above can be rewritten as follows

$$\begin{array}{rl} \dot x_1 &amp;= x_2\\ \dot x_2 &amp;= - \sin(x_1)\end{array}$$

The 2nd ODE is not merely nonlinear, it is non-polynomial (due to the sine).  However, the ODEs that model elementary chemical reactions should be polynomial due to the law of mass action. Hence, it should be impossible to simulate the simple pendulum using a chemical analog computer. Simulating the double pendulum should also be impossible.

What may be possible is to simulate an approximation. For example, if $x_1$ is sufficiently "close" to zero, then we could use the approximation $\sin(x_1) \approx x_1$, which produces a system of coupled linear (and, thus, polynomial) ODEs

$$\begin{array}{rl} \dot x_1 &amp;= x_2\\ \dot x_2 &amp;= - x_1\end{array}$$

which approximate the original pendulum provided that $x_1$ remains "small" (in absolute value).

Lastly, since concentrations cannot be negative, we have non-negativity constraints $x_1, x_2 \geq 0$.