Based on a search for multi-periodic variability among the semi-regular red variable stars in the database of the All Sky Automated Survey (ASAS), a sample of 72 typical examples is presented. Their period analysis was performed using Discrete Fourier Transform. In 41 stars we identified two significant periods each, simultaneously present, while the remaining 31 cases revealed even three such periods per star. They occur in a range roughly between 50 and 3000 days. Inter-relationships between these periods were analyzed using the double period diagram which compares adjacent periods, and the so-called Petersen diagram, the period ratio vs. the shorter period. In both diagrams we could identify six sequences of accumulation of the period values. For five of these sequences (containing 97% of all data points) we found an almost perfect coincidence with those of previous studies which were based on very different samples of semi-regular red variables. Therefore, existence and locations of these sequences in the diagrams seem to be universal features, which appear in any data set of semi-regularly variable red giants of the AGB; we conclude that they are caused by different pulsation modes as the typical and consistent properties of similar stellar AGB configurations. Stellar pulsations can be considered as the principal cause of the observed periodic variability of these stars, and not binary, rotation of a spotted surface or other possible reasons suggested in the literature.
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