I ran the simulation for 4000 generations. This is a plot of the probability that evolves, the probability of defecting when the opponent has been cooperating recently. I am actually using a moving average of recent opponent behavior, rather than just the most recent move. My population size is 100. I have plotted here the 20th percentile, median, and 80th percentile values for the probability of an unprovoked defection.
This sure looks more like some kind of chaos, rather than anything periodic! The relaxation back to polite behavior looks nicely exponential. But that indulgence in nastiness seems to come out of nowhere.
Right now I am allowing a child's parameter to run beyond the range of its parents' values by 5 percent. It must be the case that these nasty suprises come out of these mutations. For a next experiment, I will reduce the allowable range of mutation. This should reduce the frequency of nasty surprises - so I hypothesize!