At https://phys.org/print465661093.html … a study claims the Sahara desert swings between lush and arid every 20,000 years, a cynchronism with monsoon activity. This old chestnut has been dusted down and resurrected as it involves the tilt of the earth on the Milankovitch model – and the 21,000 year cycle. It involves an analysis of the laying down of Sahara dust on sea bed off the coast of West Africa – over the last 240,000 years. They claim the Sahara swings between wet and dry at regular intervals, the monsoon system recharging itself with the direction of tilt.
The paper is published in Science Advances (January 2019) and relies on sediment cores from the ocean bottom. Apparently, they have countered earlier research from similar sediment cores (nearby) which claimed a 100,000 cycle in sync with the Ice Age frequency. The authors say they didn't accept this interval as the Sahara waxing and waning should coincide with monsoon variability which they thought was more likely at 20,000 year intervals. A 20,000 year signature is what they discovered.
This is not to say that tilt of the earth as it moves around the Sun does not influence the monsoon track. It probably does – as a background feature. Other factors come into play as changes in aridity/wetness are very often abrupt and not exponential.
See also https://tallbloke.wordpress.com/2019/01/03/study-shows-the-sahara-swung-… … and the comments are worth reading. See also related ideas at www.youtube.com/watch?v=LIAkJg8knTI&t=1918s … and https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0076514