The first Feigenbaum constant is the limiting ratio of bifurcation intervals between events in which this quantity doubles. For 10 points each:
[10h] Name this quantity that is doubled by chaos-inducing events that are marked by the splitting of paths on a bifurcation diagram as the bifurcation parameter increases.
ANSWER: period [accept period-doubling bifurcations or period-doublings]
[10m] A system that reaches chaos via period-doubling is described by this “map” that sets x sub n plus one to the product of r, x sub n, and one minus x sub n. This map shares its name with a function whose graph is the canonical example of a sigmoid curve.
ANSWER: logistic map [accept logistic function; reject “log” or “logit” or “logarithm”]
[10e] The logistic map is quadratic, and thus lacks this property possessed by functions of the form “y equals m x.”
ANSWER: linear [accept word forms like linearity]
<Benjamin Chapman, Science - Math> ~21153~ <Editor: David Bass>