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For growth rate a=0.05, one has monotone growth: As already shown, a=0.95 leads to oscillation,
and the fractional oscillations are much larger than the integer ones: At a=1.32, things get pretty irregular; fractional
iteration shows what "really lies in between": At a=1.4, one seems to enter the chaotic realm,
while the fractional chaos looks more interesting: |
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This is
confirmed by fractional iteration:
