Peter Turchin and Surgey Nefedov in the book Secular Cycles take more of an analytical approach. They look at how cycles actually played out, based on financial and other detailed records of the day. Their analysis considered eight economies, the earliest of which began in 350 B. C. E.. The pattern they found looks disturbingly like the pattern that the world has been going through since the widespread use of fossil fuels began about 1800: A civilization starts its existence when a new resource becomes available, for example by deforesting land to be used for agriculture (or in our case, finding ways fossil fuels could be used). A civilization experiences Growth for 100+ years as the population is able to grow with the new resource available to it.
Eventually the civilization reaches a Stagflation period. This happens when the civilization starts reaching limits. Population is much higher, the size of the governing class is much larger, and feedbacks like erosion and soil depletion start to play a role. In my view, Stagflation period began for the United States around 1970, when US oil production began to fall.
Turchin and Nefedov found that during the Stagflation period, population growth slows and wages stop rising. Wage disparity increases, and debt grows. The cost of food and other resources becomes more variable, and begins to spike. The level of required taxes grows, as the number of government administrators grows and as armies increase in size. (Joseph Tainter refers to this growth in government services as a product of increased complexity.)