Cycles are series of states or conditions that repeat themselves, usually after a regular or nearly regular period. Cyclic behaviour is one kind — the simplest, one could say — of oscillation. The standard mathematical model of a cycle is the periodic function.
Cycles may be due to restorative forces causing repetition as in simple harmonic motion, regularity of motion such as daily, monthly, yearly, and other astronomical cycles, or being affected by something else that has these qualities. These forces may be physical, biological, economic or social.
Although weather changes from one summer to the next and from one winter to the next, the astronomical cycles that cause seasonal changes may to a fairly good approximation undergo identical repetitions. But astronomers also concern themselves with cycles like the 11-year sunspot cycle, in which the length of one cycle may differ from the next by an amount that cannot be neglected even over a short run of just a few cycles. Correspondingly, mathematicians study both periodic functions and almost periodic functions.
Early studies of cycles are found in Vedic, Buddhist and Christian sacred books. Pythagoras' study of music and Ptolemy's motion of the planets were early scientific studies of cycles; see also interval cycle and song cycle. Early studies of cycles were generally related to astronomical, astrological and weather and climatic cycles. Copernicus, Tycho Brahe, Kepler, Newton and Einstein contributed to ever refined understanding of the motion of the planets.
In modern times economic cycles were studied by Joseph Kitchen , Clement Juglar , Simon Kuznets and Nikolai Kondratieff, each of whom has an economic cycle named after them. There has been debate about the reality of some economic cycles.
Our understanding of weather cycles being attributable to annual and monthly astronomical motions was extended by Milutin Milankovitch who showed that ice ages were closely related to variations in the Earth's orbital eccentricity, axial tilt and the precession of the equinoxes which have periods of around 100,000 years, 40,000 years and 26,000 years respectively.
General cycles research pioneers were Chizhevsky in Russia and Raymond Wheeler in the USA. Ed Dewey, who formed the Foundation for the Study of Cycles in 1942, stated that everything that had been studied had been found to have cycles present. This includes cosmology, physics, biology, geology, climate, economics, sociology, civilisation, and history in general. It was Dewey who formulated the concepts of common cycle periods, cycle synchrony and harmonically related cycle periods.
Piccardi discovered inexplicable fluctuations in the rate of chemical reactions and Takata found that a human blood test he devised varied with time and depended on the sunspot cycle. Later Simon Shnoll and other researchers at the Russian Academy of Sciences found that such cycles were simultaneously happening in the growth of single celled organisms and in radioactive decay.
Through the middle part of the 20th century Abbott claimed to measure variations in the solar constant and links between the sunspot cycle and weather cycles on earth were vehemently denied by many scientists. With the coming of the artificial satellite age we have vastly better measures of both solar output and weather around the world and these cyclic links are now firmly established and accepted.
The now defunct Foundation for the Study of Cycles in the US and CIFA in Europe and Russia are organisations set up to study cycles and fluctuating phenomena. An interdisciplinary Internet discussion group on cycles allows cycles researchers from different fields to exchange ideas and results.
Ed Dewey discovered that different disciplines often reported similar cycle periods and the phases were very similar, a principle that he called cycle synchrony. He also that these commonly reported cycle periods were often related by ratios of 2 and 3 but was unable to determine why. An explanation for this has been offered by Ray Tomes in the Harmonics Theory.