Two charts with regular peaks and troughs but only one is stationary?

Question

I'm reading Forecasting Principles and Practice section on stationarity. We are shown the following image and asked which are stationary:

Obvious seasonality rules out series (d), (h) and (i). Trends and changing levels rules out series (a), (c), (e), (f) and (i). Increasing variance also rules out (i). That leaves only (b) and (g) as stationary series.

I'm looking at the first two charts on the bottom row, g and h. Both have peaks and troughs.

Why is h considered stationary while g is not?

Answer 1

The very next paragraph says:

At first glance, the strong cycles in series (g) might appear to make it non-stationary. But these cycles are aperiodic — they are caused when the lynx population becomes too large for the available feed, so that they stop breeding and the population falls to low numbers, then the regeneration of their food sources allows the population to grow again, and so on. In the long-term, the timing of these cycles is not predictable. Hence the series is stationary.