The paper considers a spectral analysis based on Fourier transform of the time series in the temperature fluctuations in the bodies of common starlings (Sturnus vulgaris) and rats (mature Wistar males). The spectra of the periods in the starlings and rats contain the same sets of harmonics, so on this basis we can tell about a common spectrum. Interesting to note that the spectrum coincides with a previously revealed spectrum of the periods, obtained with the use of local fractal analysis by the all permutations method in the course of studies of time series of the alpha decay rate fluctuations. Despite different methods of the experimental data processing used in this work (spectral analysis based on Fourier transform and local fractal analysis by the all permutations method), as well as different raw experimental data (the temperature fluctuations and alpha-decay rate fluctuations), the same spectrum of periods was obtained. On this basis, we can consider the spectrum of periods as universal one.
The papers [
The biological periods coinciding with the periods
revealed in the spectrum of the radioactive decay rate
fluctuations were found in the motion behavior of the
experimental animals [
Unfortunately, few studies of the biological systems include thorough investigations of the periods that fall into the range from several minutes to tens of minutes. This may be explained by the fact that somewhat apparent alterations in controlled biological parameters usually take time from tens of minutes to hours, so a measurement interval of a minute or less that provides a spectrum within a range of minutes-tens-minutes is considered as a less informative and hence used rarely. The aim of the present study is to fill this gap.
Four starlings (Sturnus vulgaris) (two males and two females) were used to study the dynamics of the body temperature in birds. The birds were kept in the individual cages 35х40х30 cm at natural light.
The second part of the study was performed with the mature Wistar males (n = 14) of 280-320 g body mass. The animals were kept in the plastic cages (60х18,5х38 cm), 12 animal per a cage at permanent artificial lighting from a source with 4200 К color temperature and 1200-1500 lx intensity. The animals were distributed into three experimental groups: I – intact animals (n = 5), II – gonadectomized (n = 6) and III - animals with the combined surgical gonadectomy and adrenalectomy (n = 3). During the surgeries, the animals were anaesthesized with the intramuscular Zoletil («Virbac Sante Animale», France), 10 mg/kg of body mass.
The body temperature of starlings and rats was measured with the intraperitoneally implanted sensors DTN3-28 («EMBI RESEARCH», Novosibirsk) programmed to measure temperature once a minute in the starlings and every other minute in rats.
The most probable hormones determining the ultradian rhythmical recurrence in mammals are glucocorticosteroids produced by the adrenals and, to a lesser extent, by reproductive hormones. The ultradian variability of the secretion of the hypothalamic-pituitaryadrenal axis hormones can be explained by the presence of an oscillator controlled by the central nervous system and the mechanisms of the primary feedback. In such a way, the analysis of the alterations of the parameters of ultradian rhythms in the rats with the extirpated adrenals and testes can give a possibility to clarify the effect of the negative feedback on the formation of these biorhythms.
Fig. 1 shows an example of the experimental registration: one time series of a gonadectomized rat temperature measurements with an intraperitoneally implanted sensor DTN3-28. Measurement interval is 2 min.
D S P 38.5 36.5 36 0 8000
Time, Min
We constructed the power spectra for the time series similar to that shown at Fig. 1, the values of the spectra were summarized for the appropriate frequencies in each individual spectrum belonging to one of the groups: 1) starlings, 2) I – intact rats, 3) II – gonadectomized rats and 4) III – rats with the surgical gonadectomy and adrenalectomy. In such a way, we have obtained four power spectra. Fig.2 presents an example of them: a power spectrum for the rats group III. A rectangular insert near each peak shows its period (Х-coordinate) in minutes. All values of the periods shown at Fig.2 are recorded in an appropriate line of Table 1. Fig. 3 shows an enlarged portion of the spectrum presented at Fig.2 for the period range of up to 24 min. The spectrum is four times smoothed with a running average procedure with the use of the Poisson triangular window. The values of the periods shown at Fig.3 are included into Table 1 too. X:13.13 Y:0.1089
X:14.63 Y:0.07624
X:16.79 Y:0.176
X:18.96 Y:0.179
X:22.76 Y:0.2412 6 8 10 12 14 16 18 20 22 24
Time,min
Fig. 3. Enlarged part of the power spectrum from Fig.2 in the period range of up to 24 min
Table 1 [
Numerical values of the ENOs
A number of the modes of the Earth natural
oscillations grows exponentially with the growth of their
frequency. Therefore, the columns number 1 and 2 contain
some multitude of the periods. For example, the periods
included into the column №2 have 20 modes of natural
oscillations (7.97 min … 10.1 min), while the periods
included into the column №1 have 164 types of the
oscillations (3 min … 4 min) [
The second distinctive feature of the ENOs is that each mode of the natural oscillations is, in fact, a multiplet, that is, some set of the periods. For example, several periods - 51.5, 52.8, 53.8, 55.2, 56.3 and 58.2 min. correspond to the main mode of the spheroidal oscillations, while Table 1 contains their averaged value, 53.9 min.
Therefore, in this case, coincidence of frequencies is rather a crossing of the appropriate sets.
Important to note that the spectrum, which found in this
work coincides with a previously revealed spectrum of the
periods, obtained with the use of local fractal analysis by
the all permutations method in the course of studies of time
series of the alpha decay rate fluctuations. Despite
different methods of the experimental data processing
used in this work and in work [
In our opinion, the results of the analysis of the time series in the starlings and rats temperature fluctuations presented in Table 1 confirm the hypothesis of the universal character of the spectrum observed initially in the time series of the fluctuations of the radioactive decay rate.
The results of this work can have various practical
applications [