  Aperiodic oscillations in the sorption of H2 or D2 in metallic Pd powder have
been observed, and a novel method to confirm their deterministic rather than
random character has been devised. A theorem 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.
Both the experimental and the computed time series may be tested to detect
determinism. The result is a single number within the interval [0,2]. The test
is designed in such a way that its result is close to zero for the datasets
that are deterministic and smooth, and close to 2 for the datasets that are non
deterministic (random) or non smooth (discrete). A large variety of the test
results has been obtained for the calorimetric time series recorded in
thermokinetic oscillations, periodic and quasiperiodic, accompanying the
sorption of H2 or D2 with Pd as well as for several non oscillatory
calorimetric curves recorded in this reaction. These experimental datasets, all
coming form presumably deterministic processes, yielded the results clustering
around 0.001. On the other hand, certain databases that were presumably random
or non smooth yielded the test results from 0.7 to 1.9. Against these
benchmarks, the examined, experimental, aperiodic oscillations gave the test
results between 0.004 and 0.01, which appear to be much closer to the
deterministic behavior than to randomness. Consequently, it has been concluded
that the examined cases of aperiodic oscillations in the heat evolution
accompanying the sorption of H2 or D2 in palladium may represent an occurrence
of mathematical chaos in the behavior of this system. Further applicability and
limitations of the test have also been discussed, including its intrinsic
inability to detect determinism in discrete time series.
