A local fractal analysis by all permutations method (APM) was developed. APM-analysis of noise-like time series of alpha decay rate fluctuations made it possible to reveal the spectrum of periods in the range of 1-120 min. The connection of this spectrum with the spectrum of the Earth natural oscillations was shown, and an assumption was made about its universal character, which means that it is present in fluctuations of processes of various nature. In this work, the APM method was used to study the noise-like time series of planarium chemiluminescence fluctuations. A spectrum of periods ranging from minutes to two hours has been obtained. A detailed coincidence of the found spectrum with the spectrum that we found earlier is shown. The results of present study confirm this earlier assumption about the universal nature of the detected spectrum of periods. For the mentioned range of periods, there were shown not only the close relationship of the found spectrum with the spectrum of the Earth's natural oscillations, but also its universal character: the spectra of the periods found for fluctuation in the systems of various nature (physical, chemical, biological) always coincided with the corresponding part of the found spectrum.

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