Chaos in oscillatory sorption of hydrogen in palladium

Aperiodic oscillations in the sorption of hydrogen and deuterium in palladium have been observed. An expression relating the square of a function, with the derivative and integral with variable upper limit of the same function has been proved and proposed to be used as a base for a chaos-vs.-random test. The result of one “branch” of the test is a real number \(D \in 0,2]\) ; close to zero for the deterministic and smooth datasets, and approaching two for the random or discrete datasets. Another “branch” of the test, based on the same mathematical relation, produces two functions that appear to be convergent for deterministic and smooth datasets, but run totally divergent for random or discrete ones. The \(D\) -values yielded by deterministic time series, recorded in the periodic and quasiperiodic sorptions of H \(_{2}\) or D \(_{2}\) in Pd, are around 0.001. On the other hand, the databases that were presumably random or non-smooth yielded the test results from \(D= 0.2\) to \(D= 1.9\) . Against these benchmarks, the experimental, aperiodic oscillations scored around 0.003 in \(D\) , which is much closer to the deterministic than to a random manner.