This is absolutely incorrect, and you have no idea what you are talking about. There is no sensitive chaotic model behind this, it's completely straightforward dynamics.
The fertility rate is about 2 kids per woman now. But the generation of 20 year olds is much larger than the generation of 40 year olds. So even though the generation of 0 year olds is the same size as that of 20 year olds, in 20 years time we will have replaced a small 40 year old generation by a large 20 year old generation.
There are only two factors here: Fertility rate per woman, and death rate. This prediction is not terribly sensitive to either, and both are easy to measure accurately and on quite stable long term trajectories:
The fertility rate is about 2 kids per woman now. But the generation of 20 year olds is much larger than the generation of 40 year olds. So even though the generation of 0 year olds is the same size as that of 20 year olds, in 20 years time we will have replaced a small 40 year old generation by a large 20 year old generation.
There are only two factors here: Fertility rate per woman, and death rate. This prediction is not terribly sensitive to either, and both are easy to measure accurately and on quite stable long term trajectories:
https://ourworldindata.org/fertility-rate