It's making reference to logistic curves and how rabbit populations, which can grow exponentially, will oscillate between a low and high population size.
In short, it explains why some years there are a shit ton of rabbits, and other years, very few.
But there is no oscillation visible here, just aliasing of the lines that make it appear as if there are suddenly none. Note the "none" instead of few. Also it would still not make sense since 1 can not split into 2? And why should the generational succession get faster and faster? 9 woman get 1 child every month kind of math or what?
It doesn't, the one that aligns is the bifurcation diagram of the function used to make the set (f(z)=z^2+c), which is different from the rabbit one (the logistic map, f(x)=rx(1-x)).