
In an article Star with vast tail astonishes scientists World Science mentions the discovery of a huge tail from the star Mira which is traveling fast through the interstellar medium. This tail effectively gives a history of the stars fluctuations much like we get on Earth with tree rings or ice bores showing past climate.
I have added what looks like a cycle in Mira's tail with the red notches added to the photo.

Using the information in the article that the tail is 30,000 years of history, and the fact that there are at least 6 full cycles present, this means that the cycle will be a little less than 5,000 years. I am picking that it will turn out to be a 4,600 year cycle. Such a cycle has been found in the solar system as major alignments of the outer planets and also suggested as a climate cycle. In maps of the galaxy spiral arms I have also seen wave like structures which are repeated at about 4,600 light year intervals. These things are not well established, but are interesting areas for further study.
The manner in which the tail is formed is demonstrated in an artists reconstruction movie at NASA which is interesting to watch.
Mira is a variable star and is the classic case of its type of oscillating red giant star with period about 11 months. That type has rather irregular cycles with huge variations in brightness, from invisible to the naked eye through to a quite bright star. Individual cycles vary considerably in the limits to these extremes also. Actually there is also a companion star which orbits in around 400 years, so it has many different forms of cycle present.
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Blog of Ray Tomes research on cycles, news reports on cycles, my original research on the Harmonics Theory and discussion of these matters.
There are cycles in everything. There are cycles in the weather, the economy, the sun, wars, geological formations, atomic vibrations, climate, human moods, the motions of the planets, populations of animals, the occurrence of diseases, the prices of commodities and shares and the large scale structure of the universe. None of these are independent of each other.
Research shows that very different disciplines often find the same cycle periods in their data. The inter-relatedness of all things is an idea who's time has come. The study of cycles is an excellent way to understand this because the periods of cycles are as easy to recognise as fingerprints or DNA sequences.
"The universe, believe it or not, is nothing other than a giant musical instrument with a very special but predictable pattern of harmonically related oscillations which determine the structure of everything from galactic clusters to subatomic particles and we are just parts of the various vibration modes."
The single axiom of the Harmonics Theory is that:
The Universe consists of a standing wave which develops harmonically related standing waves and each of these does the same.