# Universality in Chua's Circuit

Since Chua's circuit appears to show the period doubling route to chaos, it is interesting to try to test the universality of this route.

Here are measurements of the capacitance (in pF) of a high precision capacitor making up part of C1 at the onset of the periodic orbits.

 Period Capacitance C1 Difference Ratio 2 1136.4 +/- 0.1 4 1104.6 +/- 0.1 31.8 +/- 0.15 8 1097.75 +/- 0.1 6.85 +/- 0.15 4.64 +/- 0.02 16 1096.0 +/- 0.1 1.75 +/- 0.15 3.9 +/- 0.1

The "Difference" column shows successive differences between the capacitance values, and the "Ratio" column shows the ratios between successive "Differences". i.e. (Cn-1 - Cn) / (Cn - Cn+1 ) .This quantity should approach the universal value = 4.6692016091.... Clearly the ratios rapidly run out of precision as the period order increases and the transitions get closer together - just where the constancy should get better! The results do however appear to be remarkably consistent (within two error bar widths) with the expected universal value.